OpenRaiser/Intern-Atlas huggingface dataset:
Towards "Propagation = Logic + Control"
Venue: arXiv cs.PL 2006
Year: 2006

Constraint propagation algorithms implement logical inference. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level framework that clearly differentiates between information needed for controlling propagation versus that needed for the logical semantics of complex constraints composed from primitive ones. We argue for the appropriateness of our controlled propagation framework by showing that it captures the underlying principles of manually designed propagation algorithms, such as literal watching for unit clause propagation and the lexicographic ordering constraint. We provide an implementation and benchmark results that demonstrate the practicality and efficiency of our framework.
ACD Term Rewriting
Venue: arXiv cs.PL 2006
Year: 2006

We introduce Associative Commutative Distributive Term Rewriting (ACDTR), a rewriting language for rewriting logical formulae. ACDTR extends AC term rewriting by adding distribution of conjunction over other operators. Conjunction is vital for expressive term rewriting systems since it allows us to require that multiple conditions hold for a term rewriting rule to be used. ACDTR uses the notion of a "conjunctive context", which is the conjunction of constraints that must hold in the context of a term, to enable the programmer to write very expressive and targeted rewriting rules. ACDTR can be seen as a general logic programming language that extends Constraint Handling Rules and AC term rewriting. In this paper we define the semantics of ACDTR and describe our prototype implementation.
Network Coding in a Multicast Switch
Venue: arXiv cs.NI 2006
Year: 2006

We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast crossbar switch. We demonstrate a traffic pattern which requires a switch speedup if coding is not allowed, whereas, with coding the speedup requirement is eliminated completely. In addition to throughput benefits, coding simplifies the characterization of the rate region. We give a graph-theoretic characterization of the rate region with fanout splitting and intra-flow coding, in terms of the stable set polytope of the 'enhanced conflict graph' of the traffic pattern. Such a formulation is not known in the case of fanout splitting without coding. We show that computing the offline schedule (i.e. using prior knowledge of the flow arrival rates) can be reduced to certain graph coloring problems. Finally, we propose online algorithms (i.e. using only the current queue occupancy information) for multicast scheduling based on our graph-theoretic formulation. In particular, we show that a maximum weighted stable set algorithm stabilizes the queues for all rates within the rate region.
LiveWN, cpu scavenging in the Grid Era
Venue: arXiv cs.DC 2006
Year: 2006

The goal of this research is to introduce an easy and versatile way to provide and use Grid resources without the need of any OS installation or middleware configuration. At the same time we provide an excellent training tool for newer Grid users and people that want to experiment, without enforcing any installation. We have been testing it thoroughly under different circumstances with firm success.
A Generic Lazy Evaluation Scheme for Exact Geometric Computations
Venue: arXiv cs.CG 2006
Year: 2006

We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most applications, hence the need for delaying the exact computations at run time until they are actually needed. Our approach is generic and extensible in the sense that it is possible to make it a library which users can extend to their own geometric objects or primitives. It involves techniques such as generic functor adaptors, dynamic polymorphism, reference counting for the management of directed acyclic graphs and exception handling for detecting cases where exact computations are needed. It also relies on multiple precision arithmetic as well as interval arithmetic. We apply our approach to the whole geometric kernel of CGAL.
On Polynomial Time Computable Numbers
Venue: arXiv cs.CC 2006
Year: 2006

It will be shown that the polynomial time computable numbers form a field, and especially an algebraically closed field.
Applications of Random Parameter Matrices Kalman Filtering in Uncertain Observation and Multi-Model Systems
Venue: arXiv cs.IT 2006
Year: 2006

This paper considers the Linear Minimum Variance recursive state estimation for the linear discrete time dynamic system with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is shown that such system can be converted to a linear dynamic system with deterministic parameter matrices but state-dependent process and measurement noises. It is proved that under mild conditions, the recursive state estimation of this system is still of the form of a modified Kalman filtering. More importantly, this result can be applied to Kalman filtering with intermittent and partial observations as well as randomly variant dynamic systems.
Parametrical Neural Networks and Some Other Similar Architectures
Venue: arXiv cs.CV 2006
Year: 2006

A review of works on associative neural networks accomplished during last four years in the Institute of Optical Neural Technologies RAS is given. The presentation is based on description of parametrical neural networks (PNN). For today PNN have record recognizing characteristics (storage capacity, noise immunity and speed of operation). Presentation of basic ideas and principles is accentuated.
Lower Bounds on the Algebraic Immunity of Boolean Functions
Venue: arXiv cs.CR 2006
Year: 2006

From the motivation of algebraic attacks to stream and block ciphers([1,2,7,13,14,15]), the concept of {\em algebraic immunity} (AI) was introduced in [21] and studied in [3,5,10,11,17,18,19,20,21]. High algebraic immunity is a necessary condition for resisting algebraic attacks. In this paper, we give some lower bounds on algebraic immunity of Boolean functions. The results are applied to give lower bounds on AI of symmetric Boolean functions and rotation symmetric Boolean functions. Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value $\lceil \frac{n}{2}\rceil$ are constructed.
The computational power of population protocols
Venue: arXiv cs.CC 2006
Year: 2006

We consider the model of population protocols introduced by Angluin et al., in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via two-way interactions in the all-pairs family of communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of two-way interaction, we also consider several variants of the model in which agents communicate by anonymous message-passing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These one-way models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these one-way models using natural subclasses of the semilinear predicates.
On an Improvement over Rényi's Equivocation Bound
Venue: arXiv cs.IT 2006
Year: 2006

We consider the problem of estimating the probability of error in multi-hypothesis testing when MAP criterion is used. This probability, which is also known as the Bayes risk is an important measure in many communication and information theory problems. In general, the exact Bayes risk can be difficult to obtain. Many upper and lower bounds are known in literature. One such upper bound is the equivocation bound due to Rényi which is of great philosophical interest because it connects the Bayes risk to conditional entropy. Here we give a simple derivation for an improved equivocation bound. We then give some typical examples of problems where these bounds can be of use. We first consider a binary hypothesis testing problem for which the exact Bayes risk is difficult to derive. In such problems bounds are of interest. Furthermore using the bounds on Bayes risk derived in the paper and a random coding argument, we prove a lower bound on equivocation valid for most random codes over memoryless channels.
Self-Stabilizing Byzantine Pulse Synchronization
Venue: arXiv cs.DC 2006
Year: 2006

The ``Pulse Synchronization'' problem can be loosely described as targeting to invoke a recurring distributed event as simultaneously as possible at the different nodes and with a frequency that is as regular as possible. This target becomes surprisingly subtle and difficult to achieve when facing both transient and permanent failures. In this paper we present an algorithm for pulse synchronization that self-stabilizes while at the same time tolerating a permanent presence of Byzantine faults. The Byzantine nodes might incessantly try to de-synchronize the correct nodes. Transient failures might throw the system into an arbitrary state in which correct nodes have no common notion what-so-ever, such as time or round numbers, and can thus not infer anything from their own local states upon the state of other correct nodes. The presented algorithm grants nodes the ability to infer that eventually all correct nodes will invoke their pulses within a very short time interval of each other and will do so regularly. Pulse synchronization has previously been shown to be a powerful tool for designing general self-stabilizing Byzantine algorithms and is hitherto the only method that provides for the general design of efficient practical protocols in the confluence of these two fault models. The difficulty, in general, to design any algorithm in this fault model may be indicated by the remarkably few algorithms resilient to both fault models. The few published self-stabilizing Byzantine algorithms are typically complicated and sometimes converge from an arbitrary initial state only after exponential or super exponential time.
On the freeze quantifier in Constraint LTL: decidability and complexity
Venue: arXiv cs.LO 2006
Year: 2006

Constraint LTL, a generalisation of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some real-time logics, but this variable-binding mechanism is quite general and ubiquitous in many logical languages (first-order temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, logics with lambda-abstraction etc.). We show that Constraint LTL over the simple domain (N,=) augmented with the freeze quantifier is undecidable which is a surprising result in view of the poor language for constraints (only equality tests). Many versions of freeze-free Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes Sigma_1^1-completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACE-completeness) or when the formulae are flat in a sense introduced in the paper. Our undecidability results are sharp (i.e. with restrictions on the number of variables) and all our complexity characterisations ensure completeness with respect to some complexity class (mainly PSPACE and EXPSPACE).
Baire Categories on Small Complexity Classes and Meager-Comeager Laws
Venue: arXiv cs.CC 2006
Year: 2006

We introduce two resource-bounded Baire category notions on small complexity classes such as P, SUBEXP, and PSPACE and on probabilistic classes such as BPP, which differ on how the corresponding finite extension strategies are computed. We give an alternative characterization of small sets via resource-bounded Banach-Mazur games. As an application of the first notion, we show that for almost every language A (i.e. all except a meager class) computable in subexponential time, P(A)=BPP(A). We also show that almost all languages in PSPACE do not have small nonuniform complexity. We then switch to the second Baire category notion (called locally-computable), and show that the class SPARSE is meager in P. We show that in contrast to the resource-bounded measure case, meager-comeager laws can be obtained for many standard complexity classes, relative to locally-computable Baire category on BPP and PSPACE. Another topic where locally-computable Baire categories differ from resource-bounded measure is regarding weak-completeness: we show that there is no weak-completeness notion in P based on locally-computable Baire categories, i.e. every P-weakly-complete set is complete for P. We also prove that the class of complete sets for P under Turing-logspace reductions is meager in P, if P is not equal to DSPACE(log n), and that the same holds unconditionally for quasi-poly time. Finally we observe that locally-computable Baire categories are incomparable with all existing resource-bounded measure notions on small complexity classes, which might explain why those two settings seem to differ so fundamentally.
Choosing Colors for Geometric Graphs via Color Space Embeddings
Venue: arXiv cs.CG 2006
Year: 2006

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored: assigning display colors to the graph's vertices. We study the additional aesthetic criterion of assigning distinct colors to vertices of a geometric graph so that the colors assigned to adjacent vertices are as different from one another as possible. We formulate this as a problem involving perceptual metrics in color space and we develop algorithms for solving this problem by embedding the graph in color space. We also present an application of this work to a distributed load-balancing visualization problem.
Primitive operations for the construction and reorganization of minimally persistent formations
Venue: arXiv cs.MA 2006
Year: 2006

In this paper, we study the construction and transformation of two-dimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations, persistence characterizes the efficacy of a directed structure of unilateral distances constraints seeking to preserve a formation shape. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequentially build any minimally persistent graph (i.e. persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the on-line reorganization of an autonomous agent formation. We prove that we can obtain any minimally persistent formation from any other one by a sequence of elementary local operations such that minimal persistence is preserved throughout the reorganization process.
Exhausting Error-Prone Patterns in LDPC Codes
Venue: arXiv cs.IT 2006
Year: 2006

It is proved in this work that exhaustively determining bad patterns in arbitrary, finite low-density parity-check (LDPC) codes, including stopping sets for binary erasure channels (BECs) and trapping sets (also known as near-codewords) for general memoryless symmetric channels, is an NP-complete problem, and efficient algorithms are provided for codes of practical short lengths n~=500. By exploiting the sparse connectivity of LDPC codes, the stopping sets of size <=13 and the trapping sets of size <=11 can be efficiently exhaustively determined for the first time, and the resulting exhaustive list is of great importance for code analysis and finite code optimization. The featured tree-based narrowing search distinguishes this algorithm from existing ones for which inexhaustive methods are employed. One important byproduct is a pair of upper bounds on the bit-error rate (BER) & frame-error rate (FER) iterative decoding performance of arbitrary codes over BECs that can be evaluated for any value of the erasure probability, including both the waterfall and the error floor regions. The tightness of these upper bounds and the exhaustion capability of the proposed algorithm are proved when combining an optimal leaf-finding module with the tree-based search. These upper bounds also provide a worst-case-performance guarantee which is crucial to optimizing LDPC codes for extremely low error rate applications, e.g., optical/satellite communications. Extensive numerical experiments are conducted that include both randomly and algebraically constructed LDPC codes, the results of which demonstrate the superior efficiency of the exhaustion algorithm and its significant value for finite length code optimization.
Matrix Games, Linear Programming, and Linear Approximation
Venue: arXiv cs.GT 2006
Year: 2006

The following four classes of computational problems are equivalent: solving matrix games, solving linear programs, best $l^{\infty}$ linear approximation, best $l^1$ linear approximation.
Automatic Identification of Document Translations in Large Multilingual Document Collections
Venue: arXiv cs.CL 2006
Year: 2006

Texts and their translations are a rich linguistic resource that can be used to train and test statistics-based Machine Translation systems and many other applications. In this paper, we present a working system that can identify translations and other very similar documents among a large number of candidates, by representing the document contents with a vector of thesaurus terms from a multilingual thesaurus, and by then measuring the semantic similarity between the vectors. Tests on different text types have shown that the system can detect translations with over 96% precision in a large search space of 820 documents or more. The system was tuned to ignore language-specific similarities and to give similar documents in a second language the same similarity score as equivalent documents in the same language. The application can also be used to detect cross-lingual document plagiarism.
On factorization and solution of multidimensional linear partial differential equations
Venue: arXiv cs.SC 2006
Year: 2006

We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations of second-order hyperbolic equations in the plane and is based on an idea given by Ulisse Dini in 1902.
Classifying extrema using intervals
Venue: arXiv cs.MS 2006
Year: 2006

We present a straightforward and verified method of deciding whether the n-dimensional point x (n>=1), such that \nabla f(x)=0, is the local minimizer, maximizer or just a saddle point of a real-valued function f. The method scales linearly with dimensionality of the problem and never produces false results.
About the Capacity of Flat and Self-Organized Ad Hoc and Hybrid Networks
Venue: arXiv cs.NI 2006
Year: 2006

Ad hoc networking specific challenges foster a strong research effort on efficient protocols design. Routing protocols based on a self-organized structure have been studied principally for the robustness and the scalability they provide. On the other hand, self-organization schemes may decrease the network capacity since they concentrate the traffic on privileged links. This paper presents four models for evaluating the capacity of a routing schemes on 802.11 like networks. Our approach consists in modeling the radio resource sharing principles of 802.11 like MAC protocols as a set of linear constraints. We have implemented two models of fairness. The first one assumes that nodes have a fair access to the channel, while the second one assumes that on the radio links. We then develop a pessimistic and an optimistic scenarii of spatial re-utilization of the medium, yielding a lower bound and an upper bound on the network capacity for each fairness case. Our models are independent of the routing protocols and provide therefore a relevant framework for their comparison. We apply our models to a comparative analysis of the well-known shortest path base flat routing protocol OLSR against two main self-organized structure approaches, VSR, and Wu & Li's protocols. This study concludes on the relevance of self-organized approaches from the network capacity point of view.
Coding for Parallel Channels: Gallager Bounds and Applications to Repeat-Accumulate Codes
Venue: arXiv cs.IT 2006
Year: 2006

This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived. The framework of the second version of the Duman and Salehi (DS2) bounds is generalized to the case of parallel channels, along with the derivation of optimized tilting measures. The connection between the generalized DS2 and the 1961 Gallager bounds, known previously for a single channel, is revisited for the case of parallel channels. The new bounds are used to obtain improved inner bounds on the attainable channel regions under ML decoding. These improved bounds are applied to ensembles of turbo-like codes, focusing on repeat-accumulate codes and their recent variations.
A State-Based Regression Formulation for Domains with Sensing Actions<br> and Incomplete Information
Venue: arXiv cs.AI 2006
Year: 2006

We present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ a three-valued characterization of domains with sensing actions to define the regression function. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one.
The Three Gap Theorem (Steinhauss Conjecture)
Venue: arXiv cs.LO 2006
Year: 2006

We deal with the distribution of N points placed consecutively around the circle by a fixed angle of a. From the proof of Tony van Ravenstein, we propose a detailed proof of the Steinhaus conjecture whose result is the following: the N points partition the circle into gaps of at most three different lengths. We study the mathematical notions required for the proof of this theorem revealed during a formal proof carried out in Coq.