pinecone/core-2020-05-10-deduplication huggingface dataset:
From Operational Semantics to Domain Theory

AbstractThis paper builds domain theoretic concepts upon an operational foundation. The basic operational theory consists of a single step reduction system from which an operational ordering and equivalence on programs are defined. The theory is then extended to include concepts from domain theory, including the notions of directed set, least upper bound, complete partial order, monotonicity, continuity, finite element,ω-algebraicity, full abstraction, and least fixed point properties. We conclude by using these concepts to construct a (strongly) fully abstract continuous model for our language. In addition we generalize a result of Milner and prove the uniqueness of such models
The Dynamic Universality of Sigmoidal Neural Networks

AbstractWe investigate the computational power of recurrent neural networks that apply the sigmoid activation functionσ(x)=[2/(1+e−x)]−1. These networks are extensively used in automatic learning of non-linear dynamical behavior. We show that in the noiseless model, there exists a universal architecture that can be used to compute any recursive (Turing) function. This is the first result of its kind for the sigmoid activation function; previous techniques only applied to linearized and truncated version of this function. The significance of our result, besides the proving technique itself, lies in the popularity of the sigmoidal function both in engineering applications of artificial neural networks and in biological modelling. Our techniques can be applied to a much more general class of “sigmoidal-like” activation functions, suggesting that Turing universality is a relatively common property of recurrent neural network models
Machine Induction without Revolutionary Changes in Hypothesis Size

AbstractThis paper provides a beginning study of the effects on inductive inference of paradigm shifts whose absence is approximately modeled by various formal approaches to forbidding large changes in the size of programs conjectured. One approach, calledseverely parsimonious, requires all the programs conjectured on the way to success to be nearly (i.e., within a recursive function of) minimal size. It is shown that this very conservative constraint allows learning infinite classes of functions, butnotinfinite r.e. classes of functions. Another approach, callednon-revolutionary, requires all conjectures to be nearly the same size as one another. This quite conservative constraint is, nonetheless, shown to permit learning some infinite r.e. classes of functions. Allowing up to one extrabounded sizemind change towards a final program learned certainly does not appear revolutionary. However, somewhat surprisingly for scientific (inductive) inference, it is shown that there are classes learnablewiththe non-revolutionary constraint (respectively, with severe parsimony), up to (i+1) mind changes, and no anomalies, which classes cannotbe learned with no size constraint, an unbounded, finite number of anomalies in the final program, but with no more thanimind changes. Hence, in some cases, the possibility of one extra mind change is considerably more liberating than removal of very conservative size shift constraints. The proofs of these results are also combinatorially interesting
Using Vapnik–Chervonenkis Dimension to Analyze the Testing Complexity of Program Segments

AbstractWe examine the complexity of testing different program constructs. We do this by defining a measure of testing complexity known as VCP-dimension, which is similar to the Vapnik–Chervonenkis dimension, and applying it to classes of programs, where all programs in a class share the same syntactic structure. VCP-dimension gives bounds on the number of test points needed to determine that a program is approximately correct, so by studying it for a class of programs we gain insight into the difficulty of testing the program construct represented by the class. We investigate the VCP-dimension of straight line code, if–then–else statements, and for loops. We also compare the VCP-dimension of nested and sequential if–then–else statements as well as that of two types of for loops with embedded if–then–else statements. Finally, we perform an empirical study to estimate the expected complexity of straight line code
More on Nonregular PDL: Finite Models and Fibonacci-like Programs

AbstractWe continue research on enriching propositional dynamic logic (PDL) with nonregular programs. Previous work indicates that the general problem of characterizing those extensions for which PDL becomes undecidable is probably very hard. After observing that any nonregular extension increases the expressive power of PDL, we concentrate on one-letter extensions. First, we address the issue of finite models: A general condition is formulated, and is proven to be sufficient for a one-letter extension to violate the finite model property. We show the condition to hold in several cases, including all polynomials, sums of primes, and linear recurrences. We then build on a technique of Paterson and Harel, and show that the validity problem for PDL enriched with any Fibonacci-like sequence isΠ11-complete
Restricted Information from Nonadaptive Queries to NP

AbstractWe investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators donothave full access to the answers to the queries but get only restricted information such as the number of queries that are in the oracle set or even just this number modulom, for somem⩾2. We also investigate the case in which evaluators are nondeterministic. We show that when we vary the information that the evaluators get, this can change the resulting power of the evaluators. We locate all these classes within levels of the Boolean hierarchy which allows us to compare the complexity of such classes
Logical Hierarchies in PTIME

AbstractWe consider the problem of finding a characterization for polynomial time computable queries on finite structures in terms of logical definability. It is well known that fixpoint logic provides such a characterization in the presence of a built-in linear order, but without linear order even very simple polynomial time queries involving counting are not expressible in fixpoint logic. Our approach to the problem is based on generalized quantifiers. A generalized quantifier isn-ary if it binds any number of formulas, but at mostnvariables in each formula. We prove that, for each natural numbern, there is a query on finite structures which is expressible in fixpoint logic, but not in the extension of first-order logic by any set ofn-ary quantifiers. It follows that the expressive power of fixpoint logic cannot be captured by adding finitely many quantifiers to first-order logic. Furthermore, we prove that, for each natural numbern, there is a polynomial time computable query which is not definable in any extension of fixpoint logic byn-ary quantifiers. In particular, this rules out the possibility of characterizing PTIME in terms of definability in fixpoint logic extended by a finite set of generalized quantifiers
Logspace and Logtime Leaf Languages

AbstractThe computation tree of a nondeterministic machineMwith inputxgives rise to aleaf stringformed by concatenating the outcomes of all the computations in the tree in lexicographical order. We may characterize problems by considering, for a particular “leaf language”Y, the set of allxfor which the leaf string ofMis contained inY. In this way, in the context of polynomial time computation, leaf languages were shown to capture many complexity classes. In this paper, we study the expressibility of the leaf language mechanism in the contexts of logarithmic space and of logarithmic time computation. We show that logspace leaf languages yield a much finer classification scheme for complexity classes than polynomial time leaf languages, capturing also many classes withinP. In contrast, logtime leaf languages basically behave like logtime reducibilities. Both cases are more subtle to handle than the polynomial time case. We also raise the issue of balanced versus nonbalanced computation trees underlying the leaf language. We indicate that it is a nontrivial problem to obtain information about the leaf string of a nonbalanced computation tree and present conditions under which it does not matter whether the computation tree is balanced or not
Model Checking Mobile Processes

AbstractWe introduce a temporal logic for the polyadicπ-calculus based on fixed point extensions of Hennessy–Milner logic. Features are added to account for parametrisation, generation, and passing of names, including the use, following Milner, of dependent sum and product to account for (unlocalised) input and output, and explicit parametrisation on names usingλ-abstraction and application. The latter provides a single name binding mechanism supporting all parametrisation needed. A proof system and decision procedure is developed based on Stirling and Walker's approach to model checking the modalμ-calculus using constants. One difficulty, for both conceptual and efficiency-based reasons, is to avoid the explicit use of theω-rule for parametrised processes. A key idea, following Hennessy and Lin's approach to deciding bisimulation for certain types of value-passing processes, is the relativisation of correctness assertions to conditions on names. Based on this idea, a proof system and a decision procedure are obtained for arbitraryπ-calculus processes with finite control,π-calculus correlates of CCS finite-state processes, avoiding the use of parallel composition in recursively defined processes
On Duality in Learning and the Selection of Learning Teams

AbstractPrevious work in inductive inference dealt mostly with finding one or several machines (IIMs) that successfully learn collections of functions. Herein we start with a class of functions and considerthe learner setof all IIMs that are successful at learning the given class. Applying this perspective to the case of team inference leads to the notion ofdiversificationfor a class of functions. This enable us to distinguish between several flavours of IIMs all of which must be represented in a team learning the given class
Probably Almost Bayes Decisions

AbstractIn this paper, we investigate the problem of classifying objects which are given by feature vectors with Boolean entries. Our aim is to “(efficiently) learn probably almost optimal classifications” from examples. A classical approach in pattern recognition uses empirical estimations of the Bayesian discriminant functions for this purpose. We analyze this approach for different classes of distribution functions of Boolean features:kth order Bahadur–Lazarsfeld expansions andkth order Chow expansions. In both cases, we obtain upper bounds for the required sample size which are small polynomials in the relevant parameters and which match the lower bounds known for these classes. Moreover, the learning algorithms are efficient
A New Research into Default Logic

AbstractIn previous papers some important properties of extensions of general default theories were given. In order to dedicate further research to default logic, a characterization of extensions is presented again and some new algorithms for reasoning tasks in default logic are presented in this paper. A class of default theories, auto-compatible default theory, is also developed. We show that the characterization and notions of compatibility and auto-compatibility, suitably applied to logic programs, yield some sufficient conditions of existence of answer sets. All these essentially develop the theories of Reiter and his followers
Visual Cryptography for General Access Structures

AbstractA visual cryptography scheme for a set P ofnparticipants is a method of encoding a secret imageSIintonshadow images called shares, where each participant in P receives one share. Certain qualified subsets of participants can “visually” recover the secret image, but other, forbidden, sets of participants have no information (in an information-theoretic sense) onSI. A “visual” recovery for a setX⊆P consists of xeroxing the shares given to the participants inXonto transparencies, and then stacking them. The participants in a qualified setXwill be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation. In this paper we propose two techniques for constructing visual cryptography schemes for general access structures. We analyze the structure of visual cryptography schemes and we prove bounds on the size of the shares distributed to the participants in the scheme. We provide a novel technique for realizingkout ofnthreshold visual cryptography schemes. Our construction forkout ofnvisual cryptography schemes is better with respect to pixel expansion than the one proposed by M. Naor and A. Shamir (Visual cryptography,in“Advances in Cryptology—Eurocrypt '94” CA. De Santis, Ed.), Lecture Notes in Computer Science, Vol. 950, pp. 1–12, Springer-Verlag, Berlin, 1995) and for the case of 2 out ofnis the best possible. Finally, we consider graph-based access structures, i.e., access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme
CPO Models for Compact GSOS Languages

AbstractIn this paper, we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail, and Meyer. The canonical model used for this purpose will be Abramsky's domain of synchronization trees, and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder. In the process of establishing the full abstraction result, we also obtain several general results on the bisimulation preorder (including a complete axiomatization for it), and give a novel operational interpretation of GSOS languages
Gap-Definability as a Closure Property

AbstractGap-definability and the gap closure operator were defined by S. Fenner, L. Fortnow and S. Kurth (J. Comput. System Sci.48, 116–148 (1994)). Few complexity classes were known at that time to be gap-definable. In this paper, we give simple characterizations of both gap-definability and the gap-closure operator, and we show that many complexity classes are gap-definable, includingP#P,P#P[1],PSPACE,EXP,NEXP,MP(Middle-bitP), andBP·⊕P. If a class is closed under union and intersection and contains ∅ andΣ*, then it is gap-definable if and only if it containsSPP; its gap-closure is the closure of this class together withSPPunder union and intersection. On the other hand, we give some examples of classes which are reasonable and gap-definable but not closed under union (resp. intersection, complement). Finally, we show that a complexity class such asPSPACEorPP, if it is not equal toSPP, contains a maximal gap-definable many–one reduction-closed subclass, which is properly betweenSPPand the class of allPSPACE-incomplete (PP-incomplete) sets with respect to containment. The gap-closure of the class of all incomplete sets inPSPACE(resp.PP) isPSPACE(resp.PP)
Computational Limits on Team Identification of Languages

AbstractA team of learning machines is a multiset of learning machines. A team is said to successfully identify a concept just in case each member of some nonempty subset, of predetermined size, of the team identifies the concept. Team identification of programs for computable functions from their graphs has been investigated by Smith. Pitt showed that this notion is essentially equivalent to function identification by a single probabilistic machine. The present paper introduces, motivates, and studies the more difficult subject of team identification of grammars for languages from positive data. It is shown that an analog of Pitt's result about equivalence of team function identification and probabilistic function identification does not hold for language identification, and the results in the present paper reveal a very complex structure for team language identification. It is also shown that for certain cases probabilistic language identification is strictly more powerful than team language identification. Proofs of many results in the present paper involve very sophisticated diagonalization arguments. Two very general tools are presented that yield proofs of new results from simple arithmetic manipulation of the parameters of known ones
Undecidable Verification Problems for Programs with Unreliable Channels

AbstractWe consider the class of finite-state systems communicating through unbounded butlossyFIFO channels (calledlossy channel systems). These systems have infinite state spaces due to the unboundedness of the channels. In an earlier paper, we showed that the problems of checking reachability, safety properties, and eventuality properties are decidable for lossy channel systems. In this paper, we show that the following problems are undecidable:•The model checking problem in propositional temporal logics such as propositional linear time temporal logic (PTL) and computation tree logic (CTL).•The problem of deciding eventuality properties with fair channels: do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions ?The results are obtained through reduction from a variant of the Post correspondence problem
Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata

AbstractWe investigate time-space tradeoffs for traversing undirected graphs, using a variety of structured models that are all variants of Cook and Rackoff's “Jumping Automata for Graphs.” Our strongest tradeoff is a quadratic lower bound on the product of time and space for graph traversal. For example, achieving linear time requires linear space, implying that depth-first search is optimal. Since our bound in fact applies to nondeterministic algorithms fornonconnectivity, it also implies that closure under complementation of nondeterministic space-bounded complexity classes is achieved only at the expense of increased time. To demonstrate that these structured models are realistic, we also investigate their power. In addition to admitting well known algorithms such as depth-first search and random walk, we show that one simple variant of this model is nearly as powerful as a Turing machine. Specifically, for general undirected graph problems, it can simulate a Turing machine with only a constant factor increase in space and a polynomial factor increase in time
On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications

AbstractWe provide a uniform framework for the study of index data structures for a two-dimensional matrixTEXT[1:n, 1:n] whose entries are drawn from an ordered alphabetΣ. An index forTEXTcan be informally seen as the two-dimensional analog of the suffix tree for a string. It allows on-line searches and statistics to be performed onTEXTby representing compactly theΘ(n3) square submatrices ofTEXTin optimalO(n2) space. We identify 4n−1families of indices forTEXT, each containing ∏ni=1(2i−1)! isomorphic data structures. We also develop techniques leading to a single algorithm that efficiently builds any index in any family inO(n2logn) time andO(n2) space. Such an algorithm improves in various respects the algorithms for the construction of the PAT tree and the Lsuffix tree. The framework and the algorithm easily generalize tod>2 dimensions. Moreover, as part of our algorithm, we provide new algorithmic tools that yield a space-efficient implementation of the “naming scheme” of R. Karpet al.(in“Proceedings, Fourth Symposium on Theory of Computing,” pp. 125–136) for strings and matrices
Symbol–Relation Grammars: A Formalism for Graphical Languages

AbstractA common approach to the formal description of pictorial and visual languages makes use of formal grammars and rewriting mechanisms. The present paper is concerned with the formalism of Symbol–Relation Grammars (SR grammars, for short). Each sentence in an SR language is composed of a set of symbol occurrences representing visual elementary objects, which are related through a set of binary relational items. The main feature of SR grammars is the uniform way they use context-free productions to rewrite symbol occurrences as well as relation items. The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques of syntactic and semantic analysis to the case of SR grammars. The paper provides an accurate analysis of the derivation mechanism and the expressive power of the SR formalism. This is necessary to fully exploit the capabilities of the model. The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families. In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes
Contextual Insertions/Deletions and Computability

AbstractWe investigate two generalizations of insertion and deletion of words, that have recently become of interest in the context of molecular computing. Given a pair of words (x, y), called a context, the (x, y)-contextual insertion of a wordvinto a worduis performed as follows. For each occurrence ofxyas a subword inu, we include in the result of the contextual insertion the words obtained by insertingvintou, betweenxandy. The (x, y)-contextual deletion operation is defined in a similar way. We study closure properties of the Chomsky families under the defined operations, contextual ins-closed and del-closed languages, and decidability of existence of solutions to equations involving these operations. Moreover, we prove that every Turing machine can be simulated by a system based entirely on contextual insertions and deletion
Searching in an Unknown Environment: An Optimal Randomized Algorithm for the Cow-Path Problem

AbstractSearching for a goal is a central and extensively studied problem in computer science. In classical searching problems, the cost of a search function is simply the number of queries made to an oracle that knows the position of the goal. In many robotics problems, as well as in problems from other areas, we want to charge a cost proportional to the distance between queries (e.g., the time required to travel between two query points). With this cost function in mind, the abstract problem known as thew-lane cow-path problem was designed. There are known optimal deterministic algorithms for the cow-path problem; we give the first randomized algorithm in this paper. We show that our algorithm is optimal for two paths (w=2) and give evidence that it is optimal for larger values ofw. Subsequent to the preliminary version of this paper, Kaoet al.(in“Proceedings, 5th ACM–SIAM Symposium on Discrete Algorithm,” pp. 372–381, 1994) have shown that our algorithm is indeed optimal for allw⩾2. Our randomized algorithm gives expected performance that is almost twice as good as is possible with a deterministic algorithm. For the performance of our algorithm, we also derive the asymptotic growth with respect tow—despite similar complexity results for related problems, it appears that this growth has never been analyzed