Factor versus palindromic complexity of uniformly recurrent infinite words We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n) + P(n + 1) ≤ ∆C(n) + 2, for all n ∈ N. For a large class of words it is a better estimate of the palindromic complexity in terms of the factor complexity then the one presented in [2] . We provide several examples of infinite words for which our estimate reaches its upper bound. In particular, we derive an explicit prescription for the palindromic complexity of infinite words coding r-interval exchange transformations. If the permutation π connected with the transformation is given by π(k) = r + 1 − k for all k, then there is exactly one palindrome of every even length, and exactly r palindromes of every odd length. Recently, palindromes have become a popular subject of study in the field of combinatorics on infinite words. Recall that a palindrome is a word which remains unchanged if read backwards. In natural language it is for example the word "madam" in English, or "krk" (neck) in Czech. We shall study infinite words u over a finite alphabet A, i.e. sequences u = (u n ) n∈N where u i ∈ A for all i ∈ N = {0, 1, 2, . . . }. A palindrome of the length n in the infinite word u is a factor p = u i u i+1 · · · u i+n−1 such that u i u i+1 · · · u i+n−1 = u i+n−1 u i+n−2 · · · u i . The attractiveness of palindromes increased when Droubay and Pirillo provided yet another equivalent definition of sturmian words using palindromes. They have shown in [14] that an infinite word u is sturmian if and only if u contains exactly one palindrome of every even length and exactly two palindromes of every odd length.. A strong motivation for the study of palindromes in infinite words appeared already before, in their application in modeling of solid materials with long-range order, the so-called quasicrystals. In 1982, Dan Shechtman et al. [22] discovered an aperiodic structure (which was formed by rapidly-quenched aluminum alloys) that has icosahedral rotational symmetry, but no three-dimensional translational invariance (see e.g. [7] ). The existence of such structures has been absolutely unexpected. Since then, many other stable and unstable aperiodic structures with crystallographically forbidden rotational symmetry were discovered; they were named quasicrystals.. Since the discovery of quasicrystals there has been an increasing interest in the study of the spectral properties of non-periodic Schrödinger operators. One can assign to an infinite word u over an alphabet A, which models a one-dimensional quasicrystal, a Schrödinger operator H acting on the Hilbert space ℓ 2 (Z) as follows (Hφ)(n) = φ(n + 1) + φ(n − 1) + V (u n )φ(n), where V : A → R is an injection and represents a potential of the operator.. Many nice properties of these operators have been shown, and they are well understood at least in the one-dimensional case. The survey papers [11] , [21] map the history of this effort. One of the main tasks is to derive the spectral properties of the Schrödinger operator H from the properties of the sequence V (u n ). The physical motivation behind this study is that the spectral properties of operators determine the conductivity of the given structure. Very roughly speaking, if the spectrum is pure point then the structure is behaving like an insulant. In case of absolutely continuous spectrum the material is becoming a conductor.. Generally, the task of describing the spectral properties of the operator with potential given by an arbitrary infinite word u is not a simple one. The relevance of the study of palindromes in the infinite words has been proven by Hof et al. [17] who showed that the operators given by words having arbitrary large palindromes have purely singular continuous spectrum.. The aim of this article is to find a relation between factor and palindromic complexity of uniformly recurrent words. Let us first introduce the basic notions which will be used in sequel.. The set of all factors of length n of an infinite word u = u 0 u 1 u 2 · · · is denoted by L n (u) = {w 1 · · · w n | ∃i ∈ N, w 1 · · · w n = u i · · · u i+n−1 } .. The set of all factors of u, including the empty word ε is called the language of u and denoted. The variability of local configurations in the word u is characterized by the factor complexity, the function C : N → N, given by the prescription. It is known that if there is an n 0 such that C(n 0 ) ≤ n 0 , then the word u is eventually periodic, i.e. there exists k ∈ N such that u k+n = u n for every n ≥ n 0 . Any aperiodic (i.e. not eventually periodic) word therefore satisfies C(n) ≥ n + 1 for every n ∈ N. Aperiodic words of minimal complexity C(n) = n + 1 are called sturmian words. For a survey of different characteristics and properties of sturmian words see [6] .. The mirror image, or reversal, of a finite word w = w 1 · · · w n is the word w = w n · · · w 1 . If the language L(u) contains with every factor w also its mirror image w, we say that L(u) is invariant under reversal.. The palindromic complexity of the infinite word u = (u n ) n∈N is a function P : N → N which counts the number of palindromes of a given length. Formally,. Trivially, one has P(n) ≤ C(n). A non-trivial result is an estimate of P(n) using C(n) provided in [2] . . Let us mention that Theorem 1.1 implies the result of [13] : The palindromic complexity of a fixed point of a primitive morphism is bounded.. In this paper we provide an estimate of P(n) of uniformly recurrent words using the first difference ∆C(n) := C(n + 1) − C(n). For words whose factor complexity is a polynomial of degree ≤ 16, this estimate is better than that of (1). Let us recall that an infinite word u is uniformly recurrent, if the gaps between consecutive occurrences of any factor w ∈ L(u) in the word u are bounded. Equivalently, if for every n ∈ N there exists R(n) ∈ N such that in an arbitrary segment of length R(n) in the word u one finds all factors of L n (u), i.e.. Let us mention that sturmian words are example of uniformly recurrent words with language closed under reversal [14] .. In section 2 we show the following theorem.. Theorem 1.2 Let u = (u n ) n∈N be an uniformly recurrent word.. (i) If L(u) is not closed under reversal, then P(n) = 0 for sufficiently large n.. (ii) If L(u) is closed under reversal, then P(n) + P(n + 1) ≤ ∆C(n) + 2 , for all n ∈ N .. It is interesting that equality in the latter estimate of the palindromic complexity holds for some known classes of infinite words, such as Arnoux-Rauzy words or fixed points of canonical substitutions associated to numeration systems with base β, where β is a Parry number [15] . We list some of these examples in section 2. In section 4 we show that the equality in the estimate is valid also for infinite words coding r-interval exchange transformation.. 2 Proof of Theorem 1.2. First we show that unboundedness of the length of palindromes in an infinite uniformly recurrent word u implies that the language of u is invariant under mirror image.. Lemma 2.1 Let u be an infinite word which is uniformly recurrent and such that lim sup n→∞ P(n) > 0. Then L(u) = L(u).. PROOF. Let n ∈ N. Consider R(n) from the definition of uniformly recurrent words. Let p be a palindrome of length greater than R(n). It contains all factors of u of length n. In the same time it contains with every factor w also its mirror image. Thus L n (u) = L n (u) for all n ∈ N.. The above lemma in fact proves (i) of Theorem 1.2. Crucial tool for the proof of (ii) is the notion of a Rauzy graph of an infinite word.. Let u = (u n ) n∈N be an infinite word, n ∈ N. The Rauzy graph Γ n of u is an oriented graph whose set of vertices is L n (u) and the set of edges is L n+1 (u).. An edge e ∈ L n+1 (u) starts at the vertex x and ends at the vertex y, if x is a prefix and y is a suffix of e.. If the word u is uniformly recurrent, the graph Γ n is strongly connected for every n ∈ N, i.e. there exists an oriented path from every vertex x to every vertex y of the graph. The main result of this paper is the estimate of the palindromic complexity of infinite words in terms of their factor complexity. We have shown in Theorem 1.2 that uniformly recurrent words with infinitely many palindromes satisfy the following relation P(n) + P(n + 1) ≤ ∆C(n) + 2 , for all n ∈ N .. It is interesting to mention that the first difference of factor complexity was already useful for estimation of the frequencies of factors. In [9] it is shown that the frequencies of factors of length n in a recurrent word take at most 3∆C(n) values.. The second part of the paper is devoted to infinite words for which P(n) + P(n + 1) in Theorem 1.2 reaches the upper bound. We cite several examples of such infinite words among the words for which the palindromic and factor complexity was known. As a new result, we derive the palindromic complexity for infinite words coding r-interval exchange transformation and prove that for this class of infinite words the equality in the estimate hold, too.. According to our knowledge all known examples of infinite words which satisfy the equality P(n) + P(n + 1) = ∆C(n) + 2 for n ∈ N have sublinear factor complexity. A known example of an infinite word with higher factor complexity are the billiard sequences on three letters, for which C(n) = n 2 + n + 1. As shown in [8] , they satisfy P(n) + P(n + 1) = 4, and thus billiard sequences do not reach the upper bound in Theorem 1.2.. The proof of Theorem 1.2 is based on the study of properties of the Rauzy graph and its behaviour with respect to the operation of mirror image on the language of the infinite word. It turns out that the Rauzy graphs of words reaching the upper bound in our estimate of palindromic complexity must have a very special form.

O O B I O O O B I O O O O O O O O B I O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O B I O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O B I O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O


Connectivity preserving transformations for higher dimensional binary images An N -dimensional digital binary image (I) is a function I : Z N → {0, 1}. I is B 3 N −1 , W 3 N −1 connected if and only if its black pixels and white pixels are each (3 N − 1)-connected. I is only B 3 N −1 connected if and only if its black pixels are (3 N − 1)-connected. For a 3-D binary image, the respective connectivity models are B 26 , W 26 and B 26 . A pair of (3 N − 1)-neighboring opposite-valued pixels is called interchangeable in a N -D binary image I, if reversing their values preserves the original connectedness. We call such an interchange to be a (3 N − 1)-local interchange. Under the above connectivity models, we show that given two binary images of n pixels/voxels each, we can transform one to the other using a sequence of (3 N − 1)-local interchanges. The specific results are as follows. Any two B 26 -connected 3-dimensional images I and J each having n black voxels are transformable using a sequence of O((c 1 + c 2 )n 2 ) 26-local interchanges. Here, c 1 and c 2 are the total number of 8-connected components in all 2-dimensional layers of I and J respectively. We also show bounds on B 26 connectivity under a different interchange model as proposed in [3] . Next, we show that any two simply connected images under the B 26 ,W 26 connectivity model and each having n black voxels are transformable using a sequence of O(n 2 ) 26-local interchanges. We generalize this result to show that any two B 3 N −1 ,W 3 N −1 -connected N -dimensional simply connected images each having n black pixels are transformable using a sequence of O(N n 2 ) (3 N − 1)-local interchanges, where N > 1. An N -dimensional digital binary image (I) is a function I : Z N → {0, 1}. We will denote any element in Z N by an N -dimensional pixel (d 1 , d 2 , . . . , d N ). We will sometimes refer to it as a high dimensional pixel. Particularly, any element in Z 3 (Z 2 ) is called a voxel (pixel). Any N -dimensional pixel p is black (white) if I(p) = 1 (I(p) = 0). We consider finitely many black N -dimensional pixels from Z N in I.

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Reliability databases in perspective Abstract-Concepts and methods used in designing modern RDB (reliability data banks) are reviewed. Taxonomies for failures and maintenance actions are not fully standardized and can cause confusion. Section II summarizes current usages. The structure of the raw data is identified as: component socket histories with competing risk. Successive sections discuss data-structure and operations on data, data analysis with and without competing risk, and the analysis of uncertainty. In the context of reliability data, the assumption that competing risks are -independent is frequently unwarranted. Models for dependent competing risk are discussed, and illustrated with examples from pressure-relief-valve data at two Swedish nuclear-power stations.Some lessons learned are:The needs of various users of reliability databases must be distinguished. The interests and requirements of a maintenance engineer are very different from those of a risk analyst or a component designer. It is unlikely that a single reliability number serves these diverse needs.The problem of analyzing reliability-data has become a problem of data compression. Years ago, analysts justifiably complained about the sparseness of reliability data. With the advent of computers, automated sensors, and condition monitoring, there is no reason for sparseness today. The problem is knowing what to collect, how to make sense of the wealth of data that one can gather, and what to do with it.To be useful, reliability data must reveal not only the probability of failure, but also the cause of failure. Thus, competing factors causing the termination of service sojourns must be quantifiable from reliability data. Failure-causes interact, and this interaction makes the problem of quantification very challenging.

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Parallel, hardware-supported interrupt handling in an event-triggered real-time operating system A common problem in event-triggered real-time systems is caused by low-priority tasks that are implemented as interrupt handlers interrupting and disturbing high-priority tasks that are implemented as threads. This problem is termed rate-monotonic priority inversion, and current software-based solutions are restricted in terms of more sophisticated scheduler features as demanded for instance by the AUTOSAR embedded-operating-system specification.We propose a hardware-based approach that makes use of a coprocessor to eliminate the potential priority inversion. By evaluating a prototypical implementation, we show that our approach both overcomes the restrictions of software approaches and introduces only a slight processing overhead in exchange for increased predictability. Besides functional correctness, timeliness is the most important property of real-time systems, since results that are delivered too late may have the same impact as incorrect ones. Thus, it is necessary that the timely completion of all tasks associated with hard deadlines can be guaranteed in advance by performing a schedulability analysis. The more predictable the overall system behavior is, the more likely it is that a schedulability analysis yields a precise and safe result.. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. CASES'09, October [11] [12] [13] [14] [15] [16] 2009 , Grenoble, France. Copyright 2009 ACM 978-1-60558-626-7/09/10 ...$10.00. We have shown that rate-monotonic priority inversion can be avoided by making use of a coprocessor as available on commodity embedded hardware like the Infineon-TriCore platform. Our hardware-supported approach shows significant conceptual advantages over previously suggested software-based solutions; these advantages include the possibility for stack-sharing, the support for multiple task activations, and multiple tasks per priority-as demanded by the AUTOSAR-embedded-OS specification, for instance. Furthermore, by evaluating an implementation of our approach for the CiAO operating system, we have shown that the concept completely avoids the disturbance caused by interrupts from lowerpriority events. Our solution only bears a slight overhead, which is a small price to pay for the increased level of predictability that is vital to any real-time system. In this section, we discuss the implications of the related problem of interrupt-overload situations and how it affects our approach, the possibility to directly execute threads and ISRs on the PCP, as well as the general applicability of our solution. The predictability issues introduced into real-time systems by interrupts are the target of a specific area of real-time-systems research. Many solutions try to ignore unwanted interrupt requests [2, 18] . For each interrupt source, parameters like minimum interarrival times, maximum arrival rates, or maximum burst lengths have to be specified; these parameters are then monitored during normal operation. Interrupt requests that do not fit within the given boundaries are treated as unwanted interrupts and are ignored. Such methods are definitely useful to prevent and bound overload situations caused by interrupts, but they do not eliminate the problems that are introduced by a bifid priority space. High-priority hard real-time tasks can still suffer disturbance by soft real-time tasks implemented as ISRs, for instance. Our solution itself is still susceptible to interrupt overload on the PCP to a certain degree. However, it is possible to additionally guard the PCP against such overload scenarios by implementing the techniques mentioned above there. The application itself, executed on the main processor, is automatically guarded against overload situations like these by the unified priority space. Since the scheduler controls every activity on the main processor, measures like the sporadic server [20] can be used to bound the time allocated to handlers of asynchronous events.. Asymmetric multiprocessing concepts have been used in the operating-systems community before, of course. Specialized coprocessors have also been used to support the operating system with certain tasks. The main target of those approaches is to maximize throughput and efficiency of the operating system, however. Popular applications are latency hiding in message-passing systems [3] or network-protocol offloading [11] , for instance. An operatingsystem kernel that offers a solution related to ours is the Spring kernel by Stankovic and Ramamritham [21] . It uses an asymmetricmultiprocessing approach where so-called front-end processors in a separated I/O subsystem are used to offload interrupt processing. That way, rate-monotonic priority inversion can effectively be avoided. The Spring kernel, however, is designed to execute tasks in a non-preemptive manner only. Thus, it is not suitable for many real-time systems-like implementations of AUTOSAR OS, for instance.. There are other approaches that try to aid the operating-system scheduler by using hardware abstractions; however, almost all of them rely on customized hardware. These approaches-including cs2 [15] , FASTCHART [13] , Silicon TRON [16] , HW-RTOS [4] , and Atalanta [22, 1] -move operating-system functionality to the hardware level by synthesizing special circuits on FPGA boards and offering that functionality on a co-processor-like basis. Some of these solutions may also prevent rate-monotonic priority inversion as a side effect, but none of them explicitly address this issue. In contrast, our approach does not implement dedicated scheduler functions in hardware; instead, we use commodity off-the-shelf hardware to implement a unified priority space (see also Section 6.3), thereby avoiding rate-monotonic priority inversion. We prototypically implemented our approach on the TriCore microcontroller platform by extending our CiAO research operating system. In the following subsections, we describe the operatingsystem environment, the relevant peculiarities of the hardware platform, and the details of the interrupt-handler implementation. For our experiments, we use a TriBoard TC1796 by Infineon, which features the TriCore TC1796 microcontroller. It is clocked at 50 MHz, resulting in an instruction cycle of 20ns. We furthermore use a Lauterbach TRACE32 hardware debugger and tracer to precisely determine all execution times on the CPU. The tracing facility, however, does not cover the PCP. Thus, for the measurements on the PCP, we toggle I/O pins and use a digital storage oscilloscope to determine the duration of the slopes at the I/O pins. We use a function generator to generate square-wave signals at various rates to mimic external events at the I/O pins of the TC1796. For our measurements, we exclusively use the internal, no-wait-state RAM of the TC1796 for both code and data.

O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A Biologically Inspired Architecture for an Autonomous and Social Robot Abstract-Lately, lots of effort has been put into the construction of robots able to live among humans. This fact has favored the development of personal or social robots, which are expected to behave in a natural way. This implies that these robots could meet certain requirements, for example, to be able to decide their own actions (autonomy), to be able to make deliberative plans (reasoning), or to be able to have an emotional behavior in order to facilitate human-robot interaction. In this paper, the authors present a bioinspired control architecture for an autonomous and social robot, which tries to accomplish some of these features. In order to develop this new architecture, authors have used as a base a prior hybrid control architecture (AD) that is also biologically inspired. Nevertheless, in the later, the task to be accomplished at each moment is determined by a fix sequence processed by the Main Sequencer. Therefore, the main sequencer of the architecture coordinates the previously programmed sequence of skills that must be executed. In the new architecture, the main sequencer is substituted by a decision making system based on drives, motivations, emotions, and self-learning, which decides the proper action at every moment according to robot's state. Consequently, the robot improves its autonomy since the added decision making system will determine the goal and consequently the skills to be executed. A basic version of this new architecture has been implemented on a real robotic platform. Some experiments are shown at the end of the paper.

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Learning AAM fitting through simulation The active appearance model (AAM) is a powerful method for modeling and segmenting deformable visual objects. The utility of the AAM stems from two fronts: its compact representation as a linear object class and its rapid fitting procedure, which utilizes fixed linear updates. Although the original fitting procedure works well for objects with restricted variability when initialization is close to the optimum, its efficacy deteriorates in more general settings, with regards to both accuracy and capture range. In this paper, we propose a novel fitting procedure where training is coupled with, and directly addresses, AAM fitting in its deployment. This is achieved by simulating the conditions of real fitting problems and learning the best set of fixed linear mappings, such that performance over these simulations is optimized. The power of the approach does not stem from an update model with larger capacity, but from addressing the whole fitting procedure simultaneously. To motivate the approach, it is compared with a number of existing AAM fitting procedures on two publicly available face databases. It is shown that this method exhibits convergence rates, capture range and convergence accuracy that are significantly better than other linear methods and comparable to a nonlinear method, whilst affording superior computational efficiency. First proposed by Edwards et al. [1] , the active appearance model (AAM) has attracted much interest in the computer vision community for modeling and segmenting deformable visual objects. The method makes ingenious use of linear subspaces, allowing a compact representation of both shape and texture. Coupled with an efficient fitting procedure, the AAM has found utility in many computer vision problems, ranging from face animation [2] and medical image analysis [3] , to industrial vision problems [4] .. The AAM's rapid fitting stems from the utility of fixed linear update models. Despite its simplicity, the linear update model has been shown to approximately capture the relationship between the AAM's texture residual and the optimal parameter updates [1, 5] . However, this relationship holds only loosely, as it depends on the current shape and texture parameters [6] . As such, extensions to AAM fitting have diverged into two camps. In the first, improved fitting performance is attained by building feature vectors that better adhere to a linear relationship with the parameter updates [7, 8] . Proponents of the second camp reformulate the analytic fitting problem such that the linear update model is better justified [6, 9, 10] . To reduce computational complexity, these methods usually make some assumptions about the forms of the analytic updates.. In this work, a new fitting procedure is proposed that couples training and testing through simulations of real fitting conditions. The method learns a set of fixed linear update models, each of which accounts for different distributions of the AAM parameters about their optimum, throughout the iterative fitting procedure. As these updates are fixed, and by virtue of their sequential application to the image, this approach affords an efficient evaluation.. The outline of this paper is as follows. In Section 2, a brief overview of related work is presented. Next, we present our approach for AAM fitting in Section 3, addressing implementation complexities in Sections 3.1 and 3.2. Empirical evaluations are presented in Section 4. We conclude in Section 5 with additional remarks and directions for future work. We have proposed a new approach to AAM fitting based on simulations of real fitting conditions. This approach boasts significant improvements over the fixed Jacobian, project-out and an efficient approximation of the simultaneous inverse-compositional methods in both convergence accuracy and rate. Furthermore, these improvements are afforded without sacrificing computational efficiency. Also, the method affords excellent generalizability, as evidenced by its high convergence rates.. Another advantage of this formulation is that the fitting procedure can be customized to the detector used for initialization. By building a set of training perturbations which adhere to a prior defined by the detector, better fitting performance may be achieved as the distribution of samples, and hence feature vectors, are more constrained than the uniform random perturbations used in this work.. Finally, it should be noted that the experiments in this work involve a 4-fold cross-validation procedure, separately over each of the databases. Although the results suggest that the proposed approach generalizes well over the types of variations within the training database, little can be said about its generalization between databases. However, such an evaluation is rarely reported in the literature due to the lack of sufficient consistent annotations (i.e. publicly available annotations for different databases are rarely in correspondence). From initial qualitative experiments we found that the performance of all methods evaluated in this work deteriorate significantly when fitting to images from a separate database. This is because the method is required to extrapolate the types of variations exhibited in the training database to those in the testing database. In order to evaluate the generalization of the proposed approach for the case of database invariant fitting, further consistent annotations must be collected. Investigations into this aspect will be the subject of future work. The AAM's intrinsic variations in shape and texture of deformable visual objects as a linear combination of basis modes of variation Please cite this article as: J. Saragih We conducted experiments on two publicly available face databases: the IMM face database [30] and the XM2VTS database [31] . The simulation learnt (SL) approach was compared against the fixed Jacobian method [5] , project-out inverse-compositional method (POIC) [6] , the efficient estimate of the simultaneous inverse-compositional method (SIC) [9] and the nonlinear discriminative (ND) method [11] . The performance of all methods was compared on these two databases, evaluated using 4-fold crossvalidation, where each database was partitioned into four parts, in such a way, that test images contain unseen subjects only.

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Impact of Sensor-Enhanced Mobility Prediction on the Design of Energy-Efficient Localization Energy efficiency and positional accuracy are often contradictive goals. We propose to decrease power consumption without sacrificing significant accuracy by developing an energy-aware localization that adapts the sampling rate to target's mobility level. In this paper, an energy-aware adaptive localization system based on signal strength fingerprinting is designed, implemented, and evaluated. Promising to satisfy an application's requirements on positional accuracy, our system tries to adapt its sampling rate to reduce its energy consumption. The contribution of this paper is fourfold. (1) We have developed a model to predict the positional error of a real working positioning engine under different mobility levels of mobile targets, estimation error from the positioning engine, processing and networking delay in the location infrastructure, and sampling rate of location information. (2) In a real test environment, our energy-saving method solves the mobility estimation error problem by utilizing additional sensors on mobile targets. The result is that we can improve the prediction accuracy by 56.34% on average, comparing to algorithms without utilizing additional sensors. (3) We further enhance our sensor-enhanced mobility prediction algorithm by detecting the target's moving foot step and then estimate the target's velocity. This method can improve the mobility prediction accuracy by 49.81% on an average, comparing to previous sensor-enhanced mobility prediction algorithm. (4) We implemented our energy-saving methods inside a working localization infrastructure and conducted performance evaluation in a real office environment. Our performance results show as much as 68.92% reduction in power consumption. Advances in sensor network technologies enable an array of applications in consumer electronics. Emerging from this trend are an increasing number of commercial and experimental deployments of sensor networks for object tracking, such as asset tracking in warehouses, patient monitoring in medical facilities, and using location to infer activities of daily living (ADL) at home. Location information of the objects is essential for these types of applications.. Traditional localization research [11, 13, 14, 17 ] concentrated on improving the accuracy of pinpointing the spatial position of a target. However, practical deployment of localization systems shows that positional accuracy and energy efficiency are of equal importance, especially in the context of sensor networks where energy is a premium. Energy efficiency of mobile units (e.g., tags or badges) attached to the tracked targets is critical for any practical deployment. A highly accurate localization system may be of little use if it requires frequent recharging of the mobile units. Therefore, both positional accuracy and energy efficiency are necessary in the design of localization systems.. Recent work addressed the issue of energy efficiency in localization systems. For examples, object-tracking sensor network systems [1, 2, 16] found that energy efficiency and positional accuracy are often two contradictory goals. By changing sampling rate 1 of location information, a localization system can trade higher energy consumption for better positional accuracy. Sampling rate here is defined as the rate at which the localization infrastructure and its mobile units are triggered to perform necessary communication and computation in determining positions. Furthermore, these systems have identified a number of basic energysaving solutions that adaptively reduce the sampling rate with little impact on positional accuracy. Their general mechanisms are to (1) detect or predict the mobility pattern of a tracked target, and (2) then dynamically adjust the sampling rate accordingly to a changing mobility pattern. For example, when a tracked target changes its position slowly, the sampling rate can be reduced for better energy conservation without losing much positional accuracy.. There are two main drawbacks in the existing solutions. First, current adaptation mechanisms, although dynamic, calculate the sampling rate based on heuristics. There is no formal analysis of positional error due to signal noise, communication delay, and sampling delay such that given the required positional error-bound specified by the applications, the system can derive the just right sampling rate to provide accurate enough position information, minimizing the sampling rate, and in turn minimizing the energy consumption.. Second, the mobility prediction of current solutions is based on the estimated position information. The velocity is obtained by taking the two most recent estimations and dividing the distance moved by the time elapsed. The predicted moving velocity is inherently inaccurate due to the position estimation errors. The adverse effect is particularly significant when the object is static. The network might continue to sample frequently thinking the object is moving due to differences between consecutive position estimations.. Furthermore, existing solutions have been implemented and tested only in simulations. Given a lack of real deployment, assessing actual performance of their solutions in real environments is difficult. In this work, we not only propose a positional error model and a mechanism to improve the mobility prediction, but also provide an implementation and evaluation of our energy-saving methods within a real localization system, tested in a real office environment. More specifically, our energy-saving methods (1) enable an application to specify an error tolerance requirement and then (2) dynamically adapt the sampling rate for quasi-optimal energy saving while meeting the application's error tolerance requirement. This paper makes the following four contributions:. We developed an accurate positional error model to predict the positional error of a real working positioning engine under different mobility levels of mobile targets, estimation error from the positioning engine, processing and networking delay in the localization infrastructure, and sampling rate of location information. This model forms the basis for developing our energy-saving methods on how to adapt sampling rate of location information while conforming to application's positional requirement. In real test environment, we found that even a small amount of estimation error from a positioning engine can significantly impact the prediction accuracy of a target's mobility, therefore, 1 Sampling rate is defined as the rate at which the localization infrastructure and its mobile units are triggered to perform necessary communication and computation in determining positions.. causing poor results in sampling rate adaptation. Our energy-saving method solves the problem by utilizing additional sensors on mobile targets. We improve our sensor-enhanced mobility prediction algorithm which utilizes the sensor as 1-bit state indicator that tells if the target is stationary or not. By detecting the target's foot step to estimate the target's velocity, we could further improve the mobility prediction accuracy by 49.81% on average, comparing to previous sensor-enhanced mobility prediction algorithm. We implemented our energy-saving methods inside a working localization infrastructure and conducted a performance evaluation in a real office environment. Our performance results shown as much as 68.92% reduction in power consumption while the positional accuracy is maintained at the same level.. The remainder of this paper is organized as follows. Section 2 formulates the energy-saving problem and develops an accurate positional error model to predict the positional accuracy in our localization system. Section 3 presents the design and implementation of our energy-saving solutions based the developed positional error model. Section 4 describes experimental setups and shows performance results of our systems in a real working environment. Section 5 discusses related work. Section 6 draws our conclusion and future work. In this paper, we present our design, implementation and evaluation of a sensor-enhanced, energyefficient adaptive localization system based on our definition of a formal positional error model that accurately predicts positional error of a real working positioning engine. Given a specified positional error tolerance from an application, our localization system can dynamically adapt the sampling rate of location information to achieve better energy saving while conforming to application's error tolerance. Furthermore, our energy-saving method utilizes additional sensors on mobile targets to solve the estimation error problem in positioning engines. We improve our sensor-enhanced mobility prediction algorithm which utilizes the sensor as 1-bit state indicator that tells if the target is stationary or not. By detecting the target's foot step to estimate the target's velocity, we could further improve the mobility prediction accuracy by 49.81% on average, comparing to previous sensor-enhanced mobility prediction algorithm. We have implemented our energy saving methods in a working localization system and conducted performance evaluation in a real office environment. Our results have shown that prediction accuracy can be improved by as much as 56.34% on average, comparing to ASCV algorithm. As the mobility level increases, our sensor-assisted adaptive sampling method reduces power consumption by as much as 68.92%.. In order to predict a more precise sampling rate, the algorithm must predict a precise estimation_error. In the current implementation, we use an average value to approximate the estimation_error in our positioning engine. However, the variance of estimation_error of fingerprinting-based positioning engine is quite large. This approximation would give a poor estimation_error and contribute to a higher non-conformance rate. To predict estimation_error more accurately we envision two future work directions.. The first direction is to lower the variance of estimation_error in our positioning engine. Then, using an average value to approximate the estimation_error in our positioning engine would give a closer estimation_error and contribute to a lower non-conformance rate. We could apply the energy conserving methods on a more accurate positioning engine with small variance of estimation_error [19] , this would result in more precise sleep_time as well and save more energy.. The second direction is to predict estimation error based on a confidence model [15] . Our future work will further improve energy efficiency in our localization system. In the current implementation, we use an average value to approximate the estimation_error in our positioning engine. However, estimation error is dynamic depending on several factors in the environment, such as coverage area, temperature, humidity, human clusters, etc. Based on a confidence model [15] , estimation error can be modeled and prediction heuristics introduced. This enables our adaptive sampling localization to determine a more precise sleep_time for better energy consumption and improved conformance to the error tolerance requirement.. Besides, our future work will extend application's requirement specification to include not only the positional error tolerance but also an energy budget for a mobile target. This can be done by creating profiles on mappings between positional error and energy consumption under different mobility levels. These profile mappings can be obtained through offline or online calibrations. Then, when applications specify their desirable energy budgets, our system can provide a positional error bound given a target mobility level. Our idea is initially inspired by the notion of adaptive sensing or adaptive sampling in sensor network research. Energy efficient design is related to mechanisms at various levels of the wireless network protocol suite. The range estimation techniques are related to the localization error estimation. Sampling rate adaptation techniques are related to the energy-aware localization. Computation reduction techniques for fingerprinting-based localization are related to the efficient localization. In the following subsections, we review and discuss how this work is relevant or complimentary to the above mentioned research domains. To evaluate our adaptive sampling methods, we have conducted experiments to show and compare the effectiveness of periodic and adaptive sampling methods by changing values in the impact factors. These impact factors are: (1) application-specified error tolerances and (2) the mobile target's mobility levels. Two performance metrics below are measured and compared:. Unit power consumption: It measures the average power consumption per second on a tracked badge using a power-saving method. We have considered two approaches to measure unit power consumption in a real working environment. The first approach is to connect a mobile badge to a power meter. The size and the weight of the power meter, however, make this approach infeasible. The second approach is to collect real data and code traces from mobile badge while it is running in a real environment and then feed the traces to a realistic power estimation tool for Taroko called PowerTOSSIM [5] . Importantly, we would like to stress that our performance results and collected traces are not based on simulation, but on real implementations. Non-conformance rate: It measures the percentage where the reported location from our localization system to an application exceeds the specified error tolerance.. Our experimental environment is on the third floor of National Taiwan University's computer science department building. We incorporated our energy-saving methods in a Zigbee-based localization system developed prior to this work and described earlier in Section 2. The floor layout of the experimental environment is shown in Fig. 5 . The triangles mark the locations of beacon nodes. They are placed approximately 6 m apart. The current mobile badge is shown in Fig. 6 .. During the experiment, a tracked person wears a mobile badge and conducts his/her activities only within the shaded area. The area includes corridors, a meeting room, a lab office, and a restroom. Table 2 shows six different scenarios with different levels of user mobility. For example, scenario #3 corresponds to relatively high user mobility of 70%. In such a scenario, a user typically walks along a corridor, bumps into a friend, and chats with him/her for a short time. Note that each scenario involves a time length of at least 15 min (900 s). A 70% user mobility level means that a user moves 70% of the time or 630 s at a leisurely walking velocity of 0.5 m/s. He/she is stationary, i.e., standing to chat with a friend, 30% of the time (270 s). Scenario #5 corresponds to a low 30% mobility case, in which a user walks to a meeting room to have a discussion with friends. He/she occasionally moves to a white board to explain an idea. However, he/she sits and listens to friends most of the time. For each of six scenarios shown in Table 2 , we run four power-saving methods repeatedly with different application error tolerance at 5, 6, 7, 8, 9, and 10 m.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web Abstract. We present a novel approach to fuzzy dl-programs under the answer set semantics, which is a tight integration of fuzzy disjunctive programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly integrated disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. We show that the new formalism faithfully extends both fuzzy disjunctive programs and fuzzy description logics, and that under suitable assumptions, reasoning in the new formalism is decidable. Furthermore, we present a polynomial reduction of certain fuzzy dl-programs to tightly integrated disjunctive dl-programs. We also provide a special case of fuzzy dl-programs for which deciding consistency and query processing have both a polynomial data complexity. The Semantic Web [1, 6] aims at an extension of the current World Wide Web by standards and technologies that help machines to understand the information on the Web so that they can support richer discovery, data integration, navigation, and automation of tasks. The main ideas behind it are to add a machine-readable meaning to Web pages, to use ontologies for a precise definition of shared terms in Web resources, to use KR technology for automated reasoning from Web resources, and to apply cooperative agent technology for processing the information of the Web.. The Semantic Web consists of several hierarchical layers, where the Ontology layer, in form of the OWL Web Ontology Language [29, 11] , is currently the highest layer of sufficient maturity. OWL consists of three increasingly expressive sublanguages, namely, OWL Lite, OWL DL, and OWL Full. OWL Lite and OWL DL are essentially very expressive description logics with an RDF syntax [11] . As shown in [9] , ontology entailment in OWL Lite (resp., OWL DL) reduces to knowledge base (un)satisfiability in the description logic SHIF (D) (resp., SHOIN (D)). As a next step in the development of the Semantic Web, one aims especially at sophisticated representation and reasoning capabilities for the Rules, Logic, and Proof layers of the Semantic Web.. Alternate address: Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria; e-mail: lukasiewicz@kr.tuwien.ac.at. In particular, there is a large body of work on integrating rules and ontologies, which is a key requirement of the layered architecture of the Semantic Web. Significant research efforts focus on hybrid integrations of rules and ontologies, called description logic programs (or dl-programs) , which are of the form KB = (L, P ), where L is a description logic knowledge base and P is a finite set of rules involving either queries to L in a loose integration (see especially [4, 5, 3] ) or concepts and roles from L as unary resp. binary predicates in a tight integration (see especially [21, 22, 16] ).. Other works explore formalisms for handling uncertainty and vagueness / imprecision in the Semantic Web. In particular, formalisms for dealing with uncertainty and vagueness in ontologies have been applied in ontology mapping and information retrieval. Vagueness and imprecision also abound in multimedia information processing and retrieval. Moreover, handling vagueness is an important aspect of natural language interfaces to the Web. There are several recent extensions of description logics, ontology languages, and dl-programs for the Semantic Web by probabilistic uncertainty and by fuzzy vagueness. In particular, dl-programs under probabilistic uncertainty and under fuzzy vagueness have been proposed in [14, 13] and [27, 28, 15] , respectively.. In this paper, we continue this line of research. We present tightly integrated fuzzy description logic programs (or simply fuzzy dl-programs) under the answer set semantics, which are a tight integration of fuzzy disjunctive programs under the answer set semantics with fuzzy generalizations of SHIF(D) and SHOIN (D). Even though there has been previous work on fuzzy positive dl-programs [27, 28] and on loosely integrated fuzzy normal dl-programs [15] , to our knowledge, this is the first approach to tightly integrated fuzzy disjunctive dl-programs (with default negation in rule bodies). The main contributions of this paper can be summarized as follows:. -We present a novel approach to fuzzy dl-programs, which is a tight integration of fuzzy disjunctive programs under the answer set semantics with fuzzy description logics. It is a generalization of the tightly integrated disjunctive dl-programs in [16] by fuzzy vagueness in both the description logic and the logic program component. -We show that the new fuzzy dl-programs have nice semantic features. In particular, all their answer sets are also minimal models, and the cautious answer set semantics faithfully extends both fuzzy disjunctive programs and fuzzy description logics. Furthermore, the new approach also does not need the unique name assumption. -As an important property, in the large class of fuzzy dl-programs that are defined over a finite number of truth values, the problems of deciding consistency, cautious consequence, and brave consequence are all decidable. -In the extended report [17] , we also present a polynomial reduction for certain fuzzy dl-programs to the tightly integrated disjunctive dl-programs in [16] . Furthermore, we delineate a special case of fuzzy dl-programs where deciding consistency and query processing have both a polynomial data complexity.. The rest of this paper is organized as follows. Section 2 recalls combination strategies and fuzzy description logics. Section 3 introduces the syntax of fuzzy dl-programs and defines their answer set semantics.. In Section 4, we analyze some semantic properties of fuzzy dl-programs under the answer set semantics. Section 5 summarizes our main results and gives an outlook on future research. Note that further results and technical details are given in the extended report [17] .

B I I I O O B I I O O B I O O O O O O O O O O O B I I O O O O O O O O O O O B I I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Rule-Based Learning Systems for Support Vector Machines Abstract. In this article, we propose some methods for deriving symbolic interpretation of data in the form of rule based learning systems by using Support Vector Machines (SVM). First, Radial Basis Function Neural Networks (RBFNN) learning techniques are explored, as is usual in the literature, since the local nature of this paradigm makes it a suitable platform for performing rule extraction. By using support vectors from a learned SVM it is possible in our approach to use any standard Radial Basis Function (RBF) learning technique for the rule extraction, whilst avoiding the overlapping between classes problem. We will show that merging node centers and support vectors explanation rules can be obtained in the form of ellipsoids and hyper-rectangles. Next, in a dual form, following the framework developed for RBFNN, we construct an algorithm for SVM. Taking SVM as the main paradigm, geometry in the input space is defined from a combination of support vectors and prototype vectors obtained from any clustering algorithm. Finally, randomness associated with clustering algorithms or RBF learning is avoided by using only a learned SVM to define the geometry of the studied region. The results obtained from a certain number of experiments on benchmarks in different domains are also given, leading to a conclusion on the viability of our proposal. When Artificial Neural Networks and general connectionist paradigms are used for constructing supervised classifiers, black-box models are produced, a significant drawback for a learning system even if the obtained performance is satisfactory for the user. With the aim of making the resulting classifier system interpretable, in the last 15 years rule extraction methods for trained neural networks have been developed [1, 5, 15, 22, 25] . In the case of Radial Basis Function Neural Networks (RBFNN) [12, 16] , proposed rule extraction algorithms [8, 10, 14] usually impose restrictions during the training phase, to largely avoid overlapping between classes or categories and thus to facilitate the knowledge extraction process.. Also, it has been demonstrated in the last decade that Support Vector Machines, (SVM) [4, 6, 12] , which are derived from the statistical learning theory by V. N. Vapnik [23] , have an excellent classification and approximation qualities on all kind of problems. However, as it is the case of artificial neural networks, models generated by these machines are difficult to understand from the point of view of the user.. In the research on rule extraction from neural networks, it has been recently argued that a fidelity-accuracy dilemma exists, hence it must be distinguished between rule extraction using neural networks and rule extraction for neural networks [24] . Main problem addressed in this work is how to translate the knowledge acquired for a learned RBFNN or SVM during a supervised training to a description in a new representing language. The new model should be functionally equivalent to the learned machine that it was derived for, so that the same outputs be obtained.. Interpretability using the geometry of learned SVM classifiers in the form of a rule-based learning system is our goal. Two novel rule extraction methods for supervised classification problems are presented based on both, prototype vectors and vectors lying on the boundaries of the classes. Prototype vectors will be obtained either, from centers of a RBFNN trained under any training regime (supervised or unsupervised) or from any clustering algorithm. They will be used as centers for the generated regions defining rules. Vectors on the frontiers of the classes will be selected from the set of support vectors obtained from a trained standard SVM for the supervised classification problem. These vectors will be used as delimiters of the regions defining rules and they will help to avoid overlapping between classes.. On the next section, the first novel algorithm based on a RBFNN generating prototype vectors is presented. RBFNN is first trained to obtain centers for the rules, next support vectors obtained from a trained standard SVM are used as classes delimiters, thus obtaining a new rule extraction method from RBFNN. This approach starting from a trained RBFNN is the most common in the literature, producing descriptions in the form of ellipsoid rules. Furthermore, the interpretation of the rules is facilitated through a second derivation in the form of hyperrectangle rules, which are even more amenable for the user. The efficient use of the knowledge associated with the support vectors due to the geometry of the input space allows this method to solve the usual problematic of overlapping between classes when extracting rules, and it imposes no restrictions on the RBF network architecture, or its training regime.. On Section 3, in a dual form, starting with support vectors selected from a trained SVM and prototype vectors generated by any clustering algorithm or even by a RBFNN, a rule extraction procedure for SVM is proposed. This method is performed independently from the hyper-parameters and kernel selection in the SVM, and from the clustering algorithm that is implemented in order to obtain the prototype centers. The rule extraction method relies only on the geometry in the input space adopted from the learning functions. Like the previous one, it produces descriptions in the form of ellipsoid and hyper-rectangle rules.. Both proposed methods use a clustering algorithm or an unsupervised learned RBFNN to determine prototype vectors for the generation of rules during the rule extraction procedure for a supervised classification problem: for the whole input space in the first presented method, and for each separated class in the second one. High variability in the results is expected, and so is observed on several data sets, since it is well known that the performance of clustering algorithms varies when initial conditions of the training are modified. As a final extension, the second algorithm was modified for the exclusive use of the information supplied by a SVM, so variability is eliminated and it is showed that it is possible to cluster data from a learned SVM. Finally, some concluding remarks are presented and future work is discussed. In this work, a rule extraction method for RBFNN, which uses as a core an algorithm for building ellipsoids based on support vectors was proposed. Based on the results obtained, it can be concluded that the extraction technique achieves consistent models with the RBFNN, without any previous requirement on either the training regime used or its architecture.. Furthermore, in order to provide SVMs with explanatory power, a method that converts the knowledge embedded in a trained SVM into a representation based on rules was developed. The experiments of the rule extraction method on data bases of different domains, show high levels of equivalence between the SVM and the extracted rule base. Table 9 . Performance values for each data base using partition scheme 3 when more user-friendly hyper-rectangle regions are used. Additionally, a new proposal has been derived that avoids randomness in the extraction rules algorithm. From the results obtained it is possible to conclude that the proposed modification indeed avoids randomness, and a consistent base of rules is obtained without process iteration.. Given the achievements of this work, future lines of research arise. For example, it would be interesting to study the ways to extend the rule extraction methods to regression problems. If this were achieved, a more versatile technique would be available for a greater number of cases. Another question that arises is the study of the possibility of using another representation language to express the new model, such as fuzzy rules generated from ellipsoids. In order to evaluate the performance of the rule extraction algorithms in this article, we carried out several experiments on data bases obtained from the UCI repository [2] . Table 1 shows the characteristics of the data bases that were used in the experiments. SVM was implemented by using the 'OSU Support Vector Machines Toolbox v3.00' software [13] . In order to validate the hypothesis about the independence of the rule extraction method with respect to the RBFNN training techniques used, two different training procedures were used: the Netlab software [17] , which uses the EM algorithm to determine the RBF centers, and the Orr software [20] , which uses forward selection.. In the rule extraction community, the fidelity, accuracy, consistency, and comprehensibility (FACC) framework [1] is usually used to evaluate the extracted rules. Consistency has not been evaluated in this work because the presented approach in its final step eliminates any type of randomness in the algorithm and a total consistency exists, so rules extracted under differing training sessions will produce the same classifications of test examples. Instead, it has been measured the overlapping between rules, showing specificity of the rules, and the coverage, measuring the generalization obtained with the extracted rules. The accuracy-fidelity dilemma [24] has not been considered and both measures are presented evaluating the rules base. Therefore, performance of the generated rules is quantified with the following measures: 1 Iris 150 4 Real 3 2 Wisconsin 699 9 Symbolic 2 3 Wine 178 13 Real 3 4 Soybean 47 35 Integer 4 5 New -Thyroid 215 5 Real 3 6 Australian 690 14 Real and symbolic 2 7 Spect 267 23 Binary 2 8 Monk1 432 6 Symbolic 2 9 Monk2 432 6 Symbolic 2 10 Monk3 432 6 Symbolic 2 11 Zoo 101 16 Symbolic 7 12 Heart 270 13 Real, symbolic, and binary 2 Tables 2-5 show the accuracy of the RBF network and the performance values of the extracted rule base obtained when interpreting RBFNN with support vectors. Results were obtained by averaging 10 runs over stratified 10-fold crossvalidation when the test set was not provided. We can observe a high agreement between the results obtained from the rule base and those obtained from the RBF network. Further, because the Orr method uses more hidden units to that based on the Netlab software to obtain better performance, it produces a higher number of rules than the latter.. When interpreting SVM with prototype vectors, Tables 6 and 7 show the prediction error of the SVM and the performance values of the extracted rule base for each problem when ellipsoid and hyper-rectangle equations are used, respectively. Results were obtained by averaging over stratified 10-fold cross-validation when a test set was not available. Prototypes to be employed in the rule extraction procedure were determined using the k-means clustering algorithm [3] . Main point to be emphasized is the very high fidelity between the rule base and the initial learned SVM with a low overlapping degree. These values indicate that the generated rule base model captures most of the information embedded in the SVM, and it is functionally equivalent to the learned SVM.. As it was expected, during the experimentation process it was observed that the quality of the solution depends on the initial values for the centers; the selection of the prototype vectors by the clustering algorithm directly affects the number and quality of the extracted rules. Therefore, it was necessary to apply the k-means algorithm several times, starting with different initial conditions, in order to chose the best cross-validation solution among all. Partition schemes introduced in Section 4 for overcoming the randomness of the clustering algorithm were evaluated on trained SVMs on the data bases of the UCI repository. Tables 8 and 9 show the results obtained using partition scheme 3, the one with better performance on the benchmarks for ellipsoid and interval type equation rules, respectively. It can be observed that the results are comparable with those obtained using k-means for selecting prototypes, with the improvement that the mixed SVM -k-means clustering algorithm was applied only once. Thus, it has been demonstrated that it is possible to obtain an adequate rule base with a single application of the rule extraction algorithm.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O


The Ring Grooming Problem The problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand has been studied by several researchers. Here we study the related ring-grooming problem of minimizing the number of add/drop locations instead of the number of rings; in a number of situations this is a better approximation to the true equipment cost. Our main result is a new lower bound for the case of uniform traffic. This allows us to prove that a certain simple algorithm for uniform traffic is, in fact, a constant-factor approximation algorithm, and it also demonstrates that known lower bounds for the general problem-in particular, the linear programming relaxation-are not within a constant factor of the optimum. We also show that our results for uniform traffic extend readily to the more practically important case of quasi-uniform traffic. Finally, we show that if the number of nodes on the ring is fixed, then ring grooming is solvable in polynomial time; however, whether ring grooming is fixed-parameter tractable is still an open question. Many of today's telecommunication networks carry traffic on a configuration known as a SONET BLSR or a SONET bidirectional ring. A number of authors [2, 5, 11, 13, 17, 18] have studied the so-called ring-loading problem, which is the problem of minimizing the number of concentric (or "stacked") SONET bidirectional rings required to carry a given amount of traffic. Some good approximation algorithms have been obtained for this problem.. The ring-loading problem has the advantage of being easy to state and amenable to rigorous analysis, but has the drawback that its cost function gives only an approximation to the true cost of building a SONET ring network. In some situations, particularly in so-called "SONET over WDM" networks, a better approximation to the cost may be obtained by defining the cost of a SONET ring to be proportional to the number of its add/drop points, that is, locations on the ring where traffic terminates (i.e., begins or ends). The idea is that at add/drop points, costly electronic multiplexers (ADMs) must be installed, whereas elsewhere one can have an "optical passthrough" or "glassthrough" whose cost is relatively negligible.. The problem of minimizing ADMs in SONET rings, which is a special case of a more general problem known as traffic grooming, has also attracted the attention of numerous researchers [7, 12, 14 -16, 19 -23] , but these articles have concentrated either on heuristics or ILP methods without any provable a priori performance bounds, or on proving bounds under special assumptions such as shortest path routing. (In the case of unidirectional rings, however, there has been some recent work on approximation algorithms [1, 9] .) Part of the reason for this dearth of theoretical results is that the ring-grooming problem appears to be more difficult to analyze than the ring-loading problem. Even in the case of uniform traffic on a bidirectional ring, the answer to the following question was not known prior to the present article: Does there exist an ␣-approximation algorithm for some absolute constant ␣? Theorem 2 below answers this question affirmatively. In fact, we show that if the traffic is K-quasi-uniform (i.e., the largest traffic demand between any two nodes is at most K times the traffic between any other two nodes), then there is an ␣-approximation algorithm with ␣ depending only on K.. We should add that our approximation algorithm is not of tremendous practical value, as its guaranteed approximation ratio is poor. More important than the algorithm itself is Theorem 1, a new lower bound that allows us to prove that our algorithm is in fact a constant-factor approximation algorithm. In certain cases, Theorem 1 is an order of magnitude better than previous bounds [O(n 3/ 2 ) vs. O(n)]. This has an important theoretical implication: If one wishes to prove that a given algorithm-either an existing algorithm or a new algorithm-is a constant-factor approximation algorithm for the general case, then one must first improve the best known lower bounds.

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Approximate local search in combinatorial optimization Local search algorithms for combinatorial optimization problems are in general of pseudopolynomial running time and polynomial-time algorithms are often not known for finding locally optimal solutions for NP-hard optimization problems. We introduce the concept of ε-local optimality and show that an ε-local optimum can be identified in time polynomial in the problem size and 1/ε whenever the corresponding neighborhood can be searched in polynomial time, for ε > 0. If the neighborhood can be searched in polynomial time for a δ-local optimum, a variation of our main algorithm produces a (δ + ε)-local optimum in time polynomial in the problem size and 1/ε. As a consequence, a combinatorial optimization problem has a fully polynomial-time approximation scheme if and only if the problem of determining a better solution-the so-called augmentation problem-has a fully polynomial-time approximation scheme.

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On parallel composition of zero-knowledge proofs with black-box quantum simulators Let L be a language decided by a constant-round Arthur-Merlin (AM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box, quantum simulator S, then L ∈ BQP. Our result also applies to any language having a three-round classical interactive proof with negligible soundness error and a black-box quantum simulator. These results in particular disallow parallel composition of certain protocols in order to reduce soundness error while maintaining zero knowledge with a black-box quantum simulator, unless BQP = N P . They generalize analogous classical results of Goldreich and Krawczyk (1990) , who showed that when S is a black-box, classical simulator, then L ∈ BPP.Our proof goes via a reduction to quantum black-box search. We show that the existence of a black-box simulator when L / ∈ BQP would imply an impossibly-good quantum search algorithm. Zero-knowledge protocols play a central role in cryptography. Such protocols allow a prover to convince a verifier that he knows a secret, without disclosing any extra information about the secret. That is, anything efficiently computable after interacting with the prover could also have been efficiently computed without the interaction.. Interactive protocols must be secure as well as round-efficient, in practice. For general interactive proofs, parallel composition is widely used to decrease the error probability without increasing the number of rounds. Therefore, for practical cryptographic applications, one is interested in parallel-composing zero-knowledge protocols while maintaining the zero-knowledge property.. Goldreich and Krawczyk [GK90] proved a result concerning the round complexity of zeroknowledge interactive proofs: only BPP languages have three-round interactive proofs with negligible soundness error which are black-box simulation zero knowledge. This precludes parallel composition of many of the well-known zero-knowledge protocols -e.g., for Graph Isomorphism, for Graph 3-Colorability and generally, for all N P [GMW91] -while maintaining black-box zero knowledge, unless the languages are in BPP. [GK90] also show that for ArthurMerlin interactive proofs -in which the verifier's messages are his fair coin tosses -the above result can be extended to protocols with any constant number of rounds.. Loosely speaking, we say that an interactive proof deciding a language L is black-box simulation zero-knowledge if there exists a probabilistic polynomial-time simulator which using any verifier V * as a black box, on inputs in L produces a probability distribution which is indistinguishable from the distribution of conversations of V * with the prover.. The development of quantum computation over recent years has significant potential influences on cryptography. Exponential speedups by quantum computers have been found for problems that play a crucial role in current cryptographic systems. In the context of zero knowledge, it is interesting to ask what would happen if one weakens the zero-knowledge requirement to say that for x ∈ L a possibly dishonest Arthur learns nothing more after interacting with the prover than what he could determine with a black-box quantum simulator, with no interaction? Perhaps black-box quantum simulators are sufficiently more powerful than classical ones that round-efficient protocols could exist for more interesting languages L. After all, Watrous has given a black-box quantum simulator for the standard three-round Graph Isomorphism protocol which succeeds with probability exactly one [W06] , whereas classical simulators for the same protocol succeed with probability only approaching one. Perhaps quantum exact simulators would be helpful in maintaining black-box zero knowledge under parallel composition.. We note that constant-round AM protocols are particularly well-motivated in the quantum setting, as Watrous has also shown that any language with an honest-verifier quantum statistical zero-knowledge protocol has a quantum statistical zero-knowledge AM protocol with exponentially small completeness error and soundness error exponentially close to 1/2 [W02] .. In this work, we prove that the quantum-simulator situation is analogous to the classicalsimulator situation studied by Goldreich and Krawczyk. Only BQP languages have constant-round AM protocols with negligible soundness error, which are black-box quantum simulation zero knowledge. 1

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