pinecone/core-2020-05-10-deduplication huggingface dataset:
Context-Free Event Domains Are Recognizable

AbstractThe possibly non-distributive event domains which arise from Winskel's event structures with binary conflict are known to coincide with the domains of configurations of Stark's trace automata. We prove that whenever the transitive reduction of the order on finite elements in an event domain is a context-free graph in the sense of Müller and Schupp, the event domain may also be generated from a finite trace automaton, where both the set of states and the concurrent alphabet are finite. We show that the set of graph grammars which generate event domains is a recursive set. We obtain altogether an effective procedure which decides from an unlabeled graph grammar whether it generates an event domain and which constructs in that case a finite trace automaton recognizing that event domain
Distributed Cooperative Bayesian Learning Strategies

AbstractThis paper addresses the issue of designing an effective distributed learning system in which a number of agent learners estimate the parameter specifying the target probability density in parallel and the population learner (for short, the p-learner) combines their outputs to obtain a significantly better estimate. Such a system is important in speeding up learning. We propose as distributed learning systems two types of thedistributed cooperative Bayesian learning strategies(DCB), in which each agent learner or the p-learner employs a probabilistic version of the Gibbs algorithm. We analyze DCBs by giving upper bounds on their average logarithmic losses for predicting probabilities of unseen data as functions of the sample size and the population size. We thereby demonstrate the effectiveness of DCBs by showing that for some probability models, they work approximately (or sometimes exactly) as well as the nondistributed optimal Bayesian strategy, achieving a significant speed-up of learning over it. We also consider the case where the hypothesis class of probability densities is hierarchically parameterized, and there is a feedback of information from the p-learner to agent learners. In this case we propose another type of DCB based on the Markov chain Monte Carlo method, which we abbreviate as HDCB, and characterize its average prediction loss in terms of the number of feedback iterations as well as the population size and the sample size. We thereby demonstrate that for the class of hierarchical Gaussian distributions HDCB works approximately as well as the nondistributed optimal Bayesian strategy, achieving a significant speed-up of learning over it
Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets

AbstractIn this paper we study the Steiner tree problem in graphs for the case when vertices as well as edges have weights associated with them. A greedy approximation algorithm based on “spider decompositions” was developed by Klein and Ravi for this problem. This algorithm provides a worst case approximation ratio of 2lnk, wherekis the number of terminals. However, the best known lower bound on the approximation ratio is (1−o(1))lnk, assuming thatNP⊈DTIME[nO(loglogn)], by a reduction from set cover. We show that for the unweighted case we can obtain an approximation factor of lnk. For the weighted case we develop a new decomposition theorem and generalize the notion of “spiders” to “branch-spiders” that are used to design a new algorithm with a worst case approximation factor of 1.5lnk. We then generalize the method to yield an approximation factor of (1.35+ε)lnk, for any constantε>0. These algorithms, although polynomial, are not very practical due to their high running time, since we need to repeatedly find many minimum weight matchings in each iteration. We also develop a simple greedy algorithm that is practical and has a worst case approximation factor of 1.6103lnk. The techniques developed for this algorithm imply a method of approximating node weighted network design problems defined by 0–1 proper functions as well. These new ideas also lead to improved approximation guarantees for the problem of finding a minimum node weighted connected dominating set. The previous best approximation guarantee for this problem was 3lnnby Guha and Khuller. By a direct application of the methods developed in this paper we are able to develop an algorithm with an approximation factor of (1.35+ε)lnnfor any fixedε>0
Basic Observables for Processes

AbstractA general approach for defining behavioral preorders over process terms as the maximal precongruences induced by basic observables is examined. Three different observables that provide information about the initial communication capabilities of processes and about the possibility that processes get engaged in divergent computations will be considered. We show that the precongruences induced by our basic observables coincide with intuitive and/or widely studied behavioral preorders. In particular, we retrieve in our setting themust preorderof De Nicola and Hennessy and thefair/should preorderintroduced by Cleaveland and Natarajan and by Brinksma, Rensink, and Vogler. A new form of testing preorder, which we callsafe-must, also emerges. The alternative characterizations we offer shed light on the differences between these pre- orders and on the role played in their definition by tests for divergence
A Lattice-Based Public-Key Cryptosystem

AbstractAjtai recently found a random class of lattices of integer points for which he could prove the following worst-case/average-case equivalence result: If there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice from the class, then there is also a probabilistic polynomial time algorithm which solves several problems related to the shortest lattice vector problem (SVP) in any n-dimensional lattice. Ajtai and Dwork then designed a public-key cryptosystem which is provably secure unless the worst case of a version of the SVP can be solved in probabilistic polynomial time. However, their cryptosystem suffers from massive data expansion because it encrypts data bit-by-bit. Here we present a public-key cryptosystem based on similar ideas, but with much less data expansion
On Cryptographic Propagation Criteria for Boolean Functions

AbstractWe determine the functions on GF(2)n which satisfy the propagation criterion of degree n−2, PC(n−2). We study subsequently the propagation criterion of degree ℓ and order k and its extended version EPC. We determine those Boolean functions on GF(2)n which satisfy PC(ℓ) of order k⩾n−ℓ−2. We show that none of them satisfies EPC(ℓ) of the same order. We finally give a general construction of nonquadratic functions satisfying EPC(ℓ) of order k. This construction uses the existence of nonlinear, systematic codes with good minimum distances and dual distances (e.g., Kerdock codes and Preparata codes)
Almost Perfect Nonlinear Power Functions on GF(2n): The Niho Case

AbstractAlmost perfect nonlinear (APN) mappings are of interest for applications in cryptography We prove for odd n and the exponent d=22r+2r−1, where 4r+1≡0modn, that the power functions xd on GF(2n) is APN. The given proof is based on a new class of permutation polynomials which might be of independent interest. Our result supports a conjecture of Niho stating that the power function xd is even maximally nonlinear or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequences of degree n and a decimation of that sequence by d takes on precisely the three values −1, −1±2(n+1)/2
Further Results on Asymmetric Authentication Schemes

AbstractThis paper derives some further results on unconditionally secure asymmetric authentication schemes. It starts by giving a general framework for constructing A2-codes, identifying many known constructions as special cases. Then a full treatment of A3-codes (A2-codes protecting against arbiter's attacks) is given, including bounds on the parameters and optimal constructions. With these models as a basis, we proceed by giving constructions of general asymmetric authentication schemes, i.e., schemes protecting against specified arbitrary sets of participants collaborating in order to cheat someone else. As a consequence, we improve upon Chaum and Roijakkers interactive construction of unconditionally secure digital signatures and present a (noninteractive) construction in the form of a code. In addition, we also show a few bounds for this general model, proving the optimality of some constructions
Multireceiver Authentication Codes: Models, Bounds, Constructions, and Extensions

AbstractMultireceiver authentication codes allow one sender to construct an authenticated message for a group of receivers such that each receiver can verify authenticity of the received message. In this paper, we give a formal definition of multireceiver authentication codes, derive information theoretic and combinatorial lower bounds on their performance, and give new efficient and flexible constructions for such codes. Finally, we extend the basic model to the case that multiple messages are sent and the case that the sender can be any member of the group
Byzantine-Resistant Total Ordering Algorithms

AbstractMulticast group communication protocols are used extensively in fault-tolerant distributed systems. For many such protocols, the acknowledgments for individual messages define a causal order on messages. Maintaining the consistency of information, replicated on several processors to protect it against faults, is greatly simplified by a total order on messages. We present algorithms that incrementally convert a causal order on messages into a total order and that tolerate both crash and Byzantine process faults. Varying compromises between latency to message ordering and resilience to faults yield four distinct algorithms. All of these algorithms use a multistage voting strategy to achieve agreement on the total order and exploit the random structure of the causal order to ensure probabilistic termination
Sentences over Integral Domains and Their Computational Complexities

AbstractLetRbe a Hilbertian domain and letKbe its fraction field. Letψ(x1,…,xn,y) be a quantifier free arithmetical formula overR. We may also takeψ(x1,…,xn,y) to be an arithmetical formula overK[x1,…,xn] and write it asψ(y). In this paper we show that ifRhas enough non-units and ∀x1…∀xn∃yψ(x1,…,xn,y), called an ∀n∃ sentence, is true inR, then ∃yψ(y) is true inK[x1,…,xn]. Also, ifR=K[T], whereKis an infinite integral domain and∀x1…∀xn∃yψ(x1,…,xn,y)is true inR, then ∃yψ(y) is true inR[x1,…,xn]. These results are applied to find the upper and lower bounds of the time complexities of various decision problems on diophantine equations with parameters and arithmetical sentences. Some of the results are: 1. The decision problem of ∀∃ sentences and diophantine equations with parameters over the ring of integers of a global field are co-NP-complete. 2. The decision problem of ∀∃ sentences over the ring of integers of a global field is NP-complete. 3. LetKbe an infinite domain, the time complexities of the decision problems of equations with parameters and ∀∃ sentences over the polynomial ringK[t] are polynomial time reducible to factoring polynomials overK. 4. The decision problem of ∀∃ sentences over all algebraic integer rings is in P. 5. The decision problem of ∀∃ sentences over all integral domains with characteristic 0 is in P. 6. The time complexity of the decision problem of ∀∃ sentences over all integral domains is polynomial time reducible to factoring integers overZand factoring polynomials over finite fields
Greibach Normal Form Transformation Revisited

AbstractWe develop a new method for placing a given context-free grammar into Greibach normal form with only polynomial increase of its size. Starting with an arbitraryε-free context-free grammarG, we transformGinto an equivalent context-free grammarHin extended Greibach normal form; i.e., in addition to rules, fulfilling the Greibach normal form properties, the grammar can have chain rules. The size ofHwill beO(|G|3), where |G| is the size ofG. Moreover, in the case thatGis chain rule free,Hwill be already in Greibach normal form. IfHis not chain rule free then we use the standard method for chain rule elimination for the transformation ofHinto Greibach normal form. The size of the constructed grammar isO(|G|4)
Discrimination by Parallel Observers: The Algorithm

AbstractThe main result of the paper is a constructive proof of the following equivalence: two pureλ-terms are observationally equivalent in the lazy concurrentλ-calculusiffthey have the same Lévy–Longo trees. An algorithm which allows to build a context discriminating any two pureλ-terms with different Lévy–Longo trees is described. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi. Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of Boudol–Laneve's contexts with multiplicities
Decidable Integration Graphs

AbstractIntegration graphsare a computational model developed in the attempt to identify simple hybrid systems with decidable analysis problems. We start with the class ofconstant slope hybrid systems(CSHS), in which the right-hand side of all differential equations is an integer constant. We refer to continuous variables whose right-hand side constants are always 1 astimers. All other continuous variables are calledintegrators. The first result shown in the paper is that simple questions such as reachability of a given state are undecidable for even this simple class of systems. To restrict the model even further, we impose the requirement that no test that refers to integrators may appear within a loop in the graph. This restricted class of CSHS is calledintegration graphs. The main results of the paper are that the reachability problem of integration graphs is decidable for two special cases: the case of a single timer and the case of a single test involving integrators. The expressive power of the integration-graphs formalism is demonstrated by showing that some typical problems studied within the context of the calculus of durations and timed statecharts can be formulated as reachability problems for restricted integration graphs, and a high fraction of these fall into the subclasses of a single timer or a single test involving integrators
On Randomization in On-Line Computation

AbstractThis paper concerns two fundamental but somewhat neglected issues, both related to the design and analysis of randomized on-line algorithms. Motivated by early results in game theory we define several types of randomized on-line algorithms, discuss known conditions for their equivalence, and give a natural example distinguishing between two kinds of randomizations. In particular, we show thatmixedrandomized memoryless paging algorithms can achieve strictly better competitive performance thanbehavioralrandomized algorithms. Next we summarize known—and derive new—“Yao principle” theorems for lower bounding competitive ratios of randomized on-line algorithms. This leads to four different theorems for bounded/unbounded and minimization/maximization problems
Malign Distributions for Average Case Circuit Complexity

AbstractIn contrast to machine models like Turing machines or random access machines, circuits are a static computational model. The internal information flow of a computation is fixed in advance, independent of the actual input. Therefore, size and depth are natural and simple measures for circuits and provide a worst-case analysis. We consider a new model in which an internal gate is evaluated as soon as its result has been determined by a partial assignment of its inputs. This way, a dynamic notion of delay is obtained which gives rise to an average case measure for the time complexity of circuits. In a previous paper we have obtained tight upper and lower bounds for the average case complexity of several basic Boolean functions. This paper examines the asymptotic average case complexity for the set of alln-ary Boolean functions. In contrast to worst case analysis a simple counting argument does not work. We prove that with respect to the uniform probability distribution almost all Boolean functions require at leastn−logn−loglognexpected time. On the other hand, there is a significantly large subset of functions that can be computed with a constant average delay. Finally, for an arbitrary Boolean function we compare its worst case and average case complexity. It is shown that for each function that requires circuit depthd, i.e. of worst-case complexityd, the expected time complexity will be at leastd−logn−logdwith respect to an explicitly defined probability distribution. In addition, a nontrivial upper bound on the complexity of such a distribution will be obtained
An Algebra for Pomsets

AbstractWe study languages for manipulatingpartially orderedstructures withduplicates(e.g., trees, lists). As a general framework, we consider thepomset(partially ordered multiset) data type. We introduce an algebra forpomsets, which generalizes traditional algebras for (nested) sets, bags, and lists. This paper is motivated by the study of the impact of different language primitives on the expressive power. We show that the use of partially ordered types increases the expressive power significantly. Surprisingly, it turns out that the algebra when restricted to both unordered (bags) and totally ordered (lists) intermediate types, yields the same expressive power as fixpoint logic with counting on relational databases. It therefore constitutes a rather robust class of relational queries. On the other hand, we obtain a characterization of PTIME queries on lists by considering only totally ordered types
A Partial Order Approach to Branching Time Logic Model Checking

AbstractPartial order techniques enable reducing the size of the state space used for model checking, thus alleviating the “state space explosion” problem. These reductions are based on selecting a subset of the enabled operations from each program state. So far, these methods have been studied, implemented, and demonstrated for assertional languages that model the executions of a program as computation sequences, in particular the linear temporal logic. The present paper shows, for the first time, how this approach can be applied to languages that model the behavior of a program as a tree. We study here partial order reductions for branching temporal logics, e.g., the logics CTL and CTL* (with the next time operator removed) and process algebra logics such as Hennesy–Milner logic (withτactions). Conditions on the selection of subset of successors from each state during the state-space construction, which guarantee reduction that preserves CTL* properties, are given. The experimental results provided show that the reduction is substantial
Dealing with Zero-Time Transitions in Axiom Systems

AbstractIn the modalization of time-dependent systems it is often useful to use the abstraction ofzero-time transitions, i.e., changes of system state that occur in a time that can be neglected with respect to the whole dynamics of system evolution. Such an abstraction, however, sometimes generates critical situations in the formal system analysis. This may lead to limitations or unnatural use of such formal analysis. In this paper we present an approach that keeps the intuitive appeal of the zero-time transition abstraction, yet maintains simplicity and generality in its use. The approach is based on considering zero-time transitions as occurring in an infinitesimal, yet nonnull time. The adopted notation is borrowed from nonstandard analysis. The approach is illustrated through Petri nets as a case of state machines and TRIO as a case of logic-based assertion language, but it can be easily applied to any formal system dealing with states, time, and transitions
The Synthesis of Language Learners

AbstractAn index for an r.e. class of languages (by definition) is a procedure which generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) is a procedure which generates a sequence of decision procedures defining the family. Studied is the metaproblem of synthesizing from indices for r.e. classes and for indexed families of languages various kinds of language learners for the corresponding classes or families indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The negative results essentially provide lower bounds for the positive results. The proofs of some of the positive results yield, as pleasant corollaries, subset-principle or tell-tale style characterizations for the learnability of the corresponding classes or families indexed. For example, the indexed families of recursive languages that can be behaviorally correctly identified from positive data are surprisingly characterized by Angluin's condition 2 (the subset principle for circumventing overgeneralization)
Efficient Threshold Circuits for Power Series

AbstractWe show that functions with convergent real power series can be well approximated by two classes of polynomial-size small-weight threshold circuits: depth-three circuits with threshold gates on all levels and depth-four circuits with threshold gates on the first two levels and AND–OR gates on the last two. This is done without restricting the input to a fixed closed subinterval of the interval of convergence of the series. We also point out that rational functions and the logarithm of x in base b can be well approximated by the same classes of circuits when both x and b are given as input
Incremental Concept Learning for Bounded Data Mining

AbstractImportant refinements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every infinite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning machine computes a sequence of hypotheses about the target concept from a positive presentation of it. With iterative learning, the learning machine, in making a conjecture, has access to its previous conjecture and the latest data items coming in. In k-bounded example-memory inference (k is a priori fixed) the learner is allowed to access, in making a conjecture, its previous hypothesis, its memory of up to k data items it has already seen, and the next element coming in. In the case of k-feedback identification, the learning machine, in making a conjecture, has access to its previous conjecture, the latest data item coming in, and, on the basis of this information, it can compute k items and query the database of previous data to find out, for each of the k items, whether or not it is in the database (k is again a priori fixed). In all cases, the sequence of conjectures has to converge to a hypothesis correctly describing the target concept. Our results are manyfold. An infinite hierarchy of more and more powerful feedback learners in dependence on the number k of queries allowed to be asked is established. However, the hierarchy collapses to 1-feedback inference if only indexed families of infinite concepts are considered, and moreover, its learning power is then equal to learning in the limit. But it remains infinite for concept classes of only infinite r.e. concepts. Both k-feedback inference and k-bounded example-memory identification are more powerful than iterative learning but incomparable to one another. Furthermore, there are cases where redundancy in the hypothesis space is shown to be a resource increasing the learning power of iterative learners. Finally, the union of at most k pattern languages is shown to be iteratively inferable