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Preservation and decomposition theorems for bounded degree structures 14

Preservation and decomposition theorems for bounded degree s...

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Harwath, Frederik Heimberg, Lucas Schweikardt, Nicole Goethe Univ Frankfurt Main Inst Informat Frankfurt Germany

ISBN: (纸本)9781450328869

We provide elementary algorithms for two preservation theorems for first-order sentences with modulo m counting quantifiers (FO+MODm) on the class C-d of all finite structures of degree at most d: For each FO+MODm-sentence that is preserved under extensions (homomorphisms) on C-d, a C-d-equivalent existential (existential-positive) FO-sentence can be constructed in 6-fold (4-fold) exponential time. For FO-sentences, the algorithm has 5-fold (4-fold) exponential time complexity. this is complemented by lower bounds showing that for FO-sentences a 3-fold exponential blow-up of the computed existential (existential-positive) sentence is unavoidable. Furthermore, we show that for an input FO-formula, a C-d-equivalent Feferman-Vaught decomposition can be computed in 3-fold exponential time. We also provide a matching lower bound.

关键词： computational logic first-order logic modulo counting quantifiers structures of bounded degree Hanf locality elementary algorithms preservation theorems existential preservation homomorphism preservation Los-Tarski Feferman-Vaught

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Pattern logics and Auxiliary Relations 14

Pattern Logics and Auxiliary Relations

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Figueira, Diego Libkin, Leonid Univ Edinburgh Edinburgh Midlothian Scotland

ISBN: (纸本)9781450328869

A common theme in the study of logics over finite structures is adding auxiliary predicates to enhance expressiveness and convey additional information. Examples include adding an order or arithmetic for capturing complexity classes, or the power of real-life declarative languages. A recent trend is to add a data-value comparison relation to words, trees, and graphs, for capturing modern data models such as XML and graph databases. Such additions often result in the loss of good properties of the underlying logic. Our goal is to show that such a loss can be avoided if we use pattern-based logics, standard in XML and graph data querying. the essence of such logics is that auxiliary relations are tested locally with respect to other relations in the structure. these logics are shown to admit strong versions of Hanf and Gaifman locality theorems, which are used to prove a homomorphism preservation theorem, and a decidability result for the satisfiability problem. We discuss applications of these results to pattern logics over data forests, and consequently to querying XML data.

关键词： First-order logic pattern finite model theory locality homomorphism preservation theorem data trees XML decidability

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Faster decision of first-order graph properties 14

Faster decision of first-order graph properties

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Williams, Ryan Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9781450328869

First-order logic captures a vast number of computational problems on graphs. We study the time complexity of deciding graph properties definable by first-order sentences in prenex normal form with k variables. the trivial algorithm for this problem runs in O(n(k)) time on n-node graphs (the big-O hides the dependence on k). Answering a question of Miklos Ajtai, we give the first algorithms running faster than the trivial algorithm, in the general case of arbitrary first-order sentences and arbitrary graphs. One algorithm runs in O(n(k-3+omega)) <= O(n(k-0.627)) time for all k >= 3, where omega < 2.373 is the n x n matrix multiplication exponent. By applying fast rectangular matrix multiplication, the algorithm can be improved further to run in n(k-1+o(1)) time, for all k >= 9. Finally, we observe that the exponent of k - 1 is optimal, under the popular hypothesis that CNF satisfiability with n variables and m clauses cannot be solved in (2 - epsilon)(n) . poly(m) time for some epsilon > 0.

关键词： first-order logic graph algorithms matrix multiplication satisfiability

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Local Temporal Reasoning 14

Local Temporal Reasoning

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Koskinen, Eric Terauchi, Tachio NYU New York NY 10003 USA Japan Adv Inst Sci & Technol Nomi Japan

ISBN: (纸本)9781450328869

We present the first method for reasoning about temporal logic properties of higher-order, infinite-data programs. By distinguishing between the finite traces and infinite traces in the specification, we obtain rules that permit us to reason about the temporal behavior of program parts via a type-and-effect system, which is then able to compose these facts together to prove the overall target property of the program. the type system alone is strong enough to derive many temporal safety properties using refinement types and temporal effects. We also show how existing techniques can be used as oracles to provide liveness information (e.g. termination) about program parts and that the type-and-effect system can combine this information with temporal safety information to derive nontrivial temporal properties. Our work has application toward verification of higher-order software, as well as modular strategies for procedural programs.

关键词： Higher-order programs formal verification temporal logic program analysis model checking

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A Decision Procedure for Satisfiability in Separation logic with Inductive Predicates 14

A Decision Procedure for Satisfiability in Separation Logic ...

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Brotherston, James Fuhs, Carsten Perez, Juan A. Navarro Gorogiannis, Nikos UCL London England Middlesex Univ London London England

ISBN: (纸本)9781450328869

We show that the satisfiability problem for the "symbolic heap" fragment of separation logic with general inductively defined predicates- which includes most fragments employed in program verification - is decidable. Our decision procedure is based on the computation of a certain fixed point from the definition of an inductive predicate, called its "base", that exactly characterises its satisfiability. A complexity analysis of our decision procedure shows that it runs, in the worst case, in exponential time. In fact, we show that the satisfiability problem for our inductive predicates is EXPTIME-complete, and becomes NP-complete when the maximum arity over all predicates is bounded by a constant. Finally, we provide an implementation of our decision procedure, and analyse its performance both on a synthetically generated set of test formulas, and on a second test set harvested from the separation logic literature. For the large majority of these test cases, our tool reports times in the low milliseconds.

关键词： separation logic inductive predicates satisfiability decision procedure

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Model Checking Existential logic on Partially Ordered Sets 14

Model Checking Existential Logic on Partially Ordered Sets

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Bova, Simone Ganian, Robert Szeider, Stefan Vienna Univ Technol Vienna Austria

ISBN: (纸本)9781450328869

We study the problem of checking whether an existential sentence (that is, a first-order sentence in prefix form built using existential quantifiers and all Boolean connectives) is true in a finite partially ordered set (in short, a poset). A poset is a reflexive, antisymmetric, and transitive digraph. the problem encompasses the fundamental embedding problem of finding an isomorphic copy of a poset as an induced substructure of another poset. Model checking existential logic is already NP-hard on a fixed poset;thus we investigate structural properties of posets yielding conditions for fixed-parameter tractability when the problem is parameterized by the sentence. We identify width as a central structural property (the width of a poset is the maximum size of a subset of pairwise incomparable elements);our main algorithmic result is that model checking existential logic on classes of finite posets of bounded width is fixed-parameter tractable. We observe a similar phenomenon in classical complexity, where we prove that the isomorphism problem is polynomial-time tractable on classes of posets of bounded width;this settles an open problem in order theory. We surround our main algorithmic result with complexity results on less restricted, natural neighboring classes of finite posets, establishing its tightness in this sense. We also relate our work with (and demonstrate its independence of) fundamental fixedparameter tractability results for model checking on digraphs of bounded degree and bounded clique-width.

关键词： Partially Ordered Sets Model Checking Width Parameterized Complexity

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computer-checked mathematics: a formal proof of the Odd Order theorem 14

Computer-checked mathematics: a formal proof of the Odd Orde...

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Mahboubi, Assia INRIA Microsoft Joint Ctr Paris France

the Odd Order theorem is a landmark result in finite group theory, due to W. Feit and J. G.

ISBN: (纸本)9781450328869

the Odd Order theorem is a landmark result in finite group theory, due to W. Feit and J. G.

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Achieving New Upper Bounds for the Hypergraph Duality Problem through logic 14

Achieving New Upper Bounds for the Hypergraph Duality Proble...

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Gottlob, Georg Malizia, Enrico Univ Oxford Dept Comp Sci Oxford OX1 3QD England Univ Calabria DIMES I-87036 Arcavacata Di Rende CS Italy

ISBN: (纸本)9781450328869

the hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs G and H, decide whether H consists precisely of all minimal transversals of G (in which case we say that G is the dual of H). this problem is equivalent to decide whether two given non-redundant monotone DNFs are dual. It is known that (DUAL) over bar, the complementary problem to DUAL, is in GC (log(2) n, PTIME), where GC(f(n), C) denotes the complexity class of all problems that after a nondeterministic guess of O(f(n)) bits can be decided ( checked) within complexity class C. It was conjectured that (DUAL) over bar is in GC(log(2) n, LOGSPACE). In this paper we prove this conjecture and actually place the (DUAL) over bar problem into the complexity class GC (log(2) n, TC0) which is a subclass of GC (log(2) n, LOGSPACE). We here refer to the logtime-uniform version of TC0, which corresponds to FO(COUNT), i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for (DUAL) over bar that requires to guess O(log(2) n) bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in FO(COUNT).

关键词： Algorithms theory

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Decidability of weak logics with deterministic transitive closure 14

Decidability of weak logics with deterministic transitive cl...

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Joint Meeting of the 23rd annual EACSL Conference on computer science logic, CSL 2014 and the 29th annual acm/ ieee symposium on logic in computer science, LICS 2014

作者： Charatonik, Witold Kieroński, Emanuel Mazowiecki, Filip Institute of Computer Science University of Wroclaw Wroclaw Poland Institute of Informatics University of Warsaw Warsaw Poland

ISBN: (纸本)9781450328869

the deterministic transitive closure operator, added to languages containing even only two variables, allows to express many natural properties of a binary relation, including being a linear order, a tree, a forest or a partial function. this makes it a potentially attractive ingredient of computer science formalisms. In this paper we consider the extension of the two-variable fragment of first-order logic by the deterministic transitive closure of a single binary relation, and prove that the satisfiability and finite satisfiability problems for the obtained logic are decidable and EXPSPACE-complete. this contrasts with the undecidability of two-variable logic with the deterministic transitive closures of several binary relations, known before. We also consider the class of universal first-order formulas in prenex form. Its various extensions by deterministic closure operations were earlier considered by other authors, leading to both decidability and undecidability *** examine this scenario in more details. Copyright © 2014 acm.

关键词： Computability and decidability

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proceedings of the 2012 27th annual acm/ieee symposium on logic in computer science, LICS 2012: Foreword

Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Lo...

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proceedings of the 2012 27th annual acm/ieee symposium on logic in computer science, LICS 2012 2012年 x-xi页

作者： Dershowitz, Nachum Tel Aviv University Israel

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