2012 27th Annual IEEE Symposium on Logic in Computer Science最新文献

{"title":"Lower Bounds for Existential Pebble Games and k-Consistency Tests","authors":"Christoph Berkholz","doi":"10.1109/LICS.2012.14","DOIUrl":"https://doi.org/10.1109/LICS.2012.14","url":null,"abstract":"The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can easily be determined in polynomial time, where the degree of the polynomial is linear in k. We show that this linear dependence on the parameter k is necessary by proving an unconditional polynomial lower bound for determining the winner in the existential k-pebble game on finite structures. Establishing strong k-consistency is a well-known heuristic for solving the constraint satisfaction problem (CSP). By the game characterization of Kolaitis and Vardi our result implies a lower bound on every algorithm that decides if strong k-consistency can be established for a given CSP-instance.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128160156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Delta-Decidability over the Reals","authors":"Sicun Gao, J. Avigad, E. Clarke","doi":"10.1109/LICS.2012.41","DOIUrl":"https://doi.org/10.1109/LICS.2012.41","url":null,"abstract":"Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any sentence A containing only bounded quantifiers and functions in F, and any positive rational number delta, decides either “A is true”, or “a delta-strengthening of A is false”. Moreover, if F can be computed in complexity class C, then under mild assumptions, this “delta-decision problem” for bounded Sigma k-sentences resides in Sigma k(C). The results stand in sharp contrast to the well-known undecidability of the general first-order theories with these functions, and serve as a theoretical basis for the use of numerical methods in decision procedures for formulas over the reals.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129929605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Combining Deduction Modulo and Logics of Fixed-Point Definitions","authors":"David Baelde, G. Nadathur","doi":"10.1109/LICS.2012.22","DOIUrl":"https://doi.org/10.1109/LICS.2012.22","url":null,"abstract":"Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of recursive specifications. These specifications are not directly complemented by fixed-point reasoning techniques and, correspondingly, do not have to satisfy strong monotonicity restrictions. We show how to incorporate a rewriting capability into logics of fixed-point definitions towards additionally supporting recursive specifications. Specifically, we describe a natural deduction calculus that adds a form of \"closed-world'' equality - a key ingredient to supporting fixed-point definitions - to deduction modulo, a framework for extending a logic with a rewriting layer operating on formulas. We show that our calculus enjoys strong normalizability when the rewrite system satisfies general properties and we demonstrate its usefulness in specifying and reasoning about syntax-based descriptions. Our integration of closed-world equality into deduction modulo is based on an elimination principle for this form of equality that, for the first time, allows us to require finiteness of proofs without sacrificing stability under reduction.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121290520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Where First-Order and Monadic Second-Order Logic Coincide","authors":"Michael Elberfeld, Martin Grohe, Till Tantau","doi":"10.1145/2946799","DOIUrl":"https://doi.org/10.1145/2946799","url":null,"abstract":"We study on which classes of graphs first-order logic (FO) and monadic second-order logic (MSO) have the same expressive power. We show that for each class of graphs that is closed under taking subgraphs, FO and MSO have the same expressive power on the class if, and only if, it has bounded tree depth. Tree depth is a graph invariant that measures the similarity of a graph to a star in a similar way that tree width measures the similarity of a graph to a tree. For classes just closed under taking induced subgraphs, we show an analogous result for guarded second-order logic (GSO), the variant of MSO that not only allows quantification over vertex sets but also over edge sets. A key tool in our proof is a Feferman-Vaught-type theorem that is constructive and still works for unbounded partitions.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130652333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-definability of Languages by Generalized First-order Formulas over (N,+)","authors":"Andreas Krebs, A. Sreejith","doi":"10.1109/LICS.2012.55","DOIUrl":"https://doi.org/10.1109/LICS.2012.55","url":null,"abstract":"We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition predicate are also definable with the order predicate as the only numerical predicate. Let S be a subset of monoids. Let L be the logic closed under quantification over the monoids in S. Then we prove that L[<;,+] and L[<;] define the same neutral letter languages. Our result can be interpreted as the Crane Beach conjecture to hold for the logic L[<;,+]. As a consequence we get the result of Roy and Straubing that FO+MOD[<;,+] collapses to FO+MOD[<;]. For cyclic groups, we answer an open question of Roy and Straubing, proving that MOD[<;,+] collapses to MOD[<;]. Our result also shows that multiplication as a numerical predicate is necessary for Barrington's theorem to hold and also to simulate majority quantifiers. All these results can be viewed as separation results for highly uniform circuit classes. For example we separate FO[<;,+]-uniform CC0 from FO[<;,+]-uniform ACC0.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123759214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Strong Complementarity and Non-locality in Categorical Quantum Mechanics","authors":"B. Coecke, Ross Duncan, A. Kissinger, Quanlong Wang","doi":"10.1109/LICS.2012.35","DOIUrl":"https://doi.org/10.1109/LICS.2012.35","url":null,"abstract":"Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here. Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity. Since our main results are expressed in the (diagrammatic) language of dagger-compact categories, they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory. The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126546420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inductive Types in Homotopy Type Theory","authors":"S. Awodey, N. Gambino, Kristina Sojakova","doi":"10.1109/LICS.2012.21","DOIUrl":"https://doi.org/10.1109/LICS.2012.21","url":null,"abstract":"Homotopy type theory is an interpretation of Martin-Lof's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof scripts for this verification form an essential component of this research.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115647169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automatic Sequences and Zip-Specifications","authors":"C. Grabmayer, J. Endrullis, D. Hendriks, J. Klop, L. Moss","doi":"10.1109/LICS.2012.44","DOIUrl":"https://doi.org/10.1109/LICS.2012.44","url":null,"abstract":"We consider infinite sequences of symbols, also known as streams, and the decidability question for equality of streams defined in a restricted format. (Some formats lead to undecidable equivalence problems.) This restricted format consists of prefixing a symbol at the head of a stream, of the stream function `zip', and recursion variables. Here `zip' interleaves the elements of two streams alternatingly. The celebrated Thue- Morse sequence is obtained by the succinct `zip-specification' M = 0 : X X = 1 : zip(X, Y) Y = 0 : zip(Y, X) The main results are as follows. We establish decidability of equivalence of zip-specifications, by employing bisimilarity of observation graphs based on a suitably chosen cobasis. Furthermore, our analysis, based on term rewriting and coalgebraic techniques, reveals an intimate connection between zip-specifications and automatic sequences. This leads to a new and simple characterization of automatic sequences. The study of zip-specifications is placed in a wider perspective by employing observation graphs in a dynamic logic setting, yielding yet another alternative characterization of automatic sequences. By the first characterization result, zip-specifications can be perceived as a term rewriting syntax for automatic sequences. For streams σ the following are equivalent: (a) σ can be specified using zip; (b) σ is 2-automatic; and (c) σ has a finite observation graph using the cobasis (hd, even, odd). Here even and odd are defined by even(a : s) = a : odd(s), and odd(a : s) = even(s). The generalization to zip-k specifications (with zip-k interleaving k streams) and to k-automaticity is straightforward. As a natural extension of the class of automatic sequences, we also consider `zip-mix' specifications that use zips of different arities in one specification. The corresponding notion of automaton employs a state-dependent input-alphabet, with a number representation (n)A = dm ... d0 where the base of digit di is determined by the automaton A on input di-1 ... d0. Finally we show that equivalence is undecidable for a simple extension of the zip-mix format with projections analogous to even and odd.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126751013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Perfect Model for Bounded Verification","authors":"J. Esparza, P. Ganty, R. Majumdar","doi":"10.1109/LICS.2012.39","DOIUrl":"https://doi.org/10.1109/LICS.2012.39","url":null,"abstract":"A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the language generated by the system is disjoint from the language of bad traces. Regular languages are perfect, but because the disjointness problem for context-free languages is undecidable, no class containing them can be perfect. In practice, verification problems for language classes that are not perfect are often under-approximated by checking if the property holds for all behaviors of the system belonging to a fixed subset. A general way to specify a subset of behaviors is by using bounded languages. A class of languages C is perfect modulo bounded languages if it is closed under Boolean operations relative to every bounded language, and if the emptiness problem is decidable relative to every bounded language. We consider finding perfect classes of languages modulo bounded languages. We show that the class of languages accepted by multi-head pushdown automata are perfect modulo bounded languages, and characterize the complexities of decision problems. We also show that bounded languages form a maximal class for which perfection is obtained. We show that computations of several known models of systems, such as recursive multi-threaded programs, recursive counter machines, and communicating finite-state machines can be encoded as multi-head pushdown automata, giving uniform and optimal underapproximation algorithms modulo bounded languages.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"29 18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127395756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mean-Payoff Pushdown Games","authors":"K. Chatterjee, Yaron Velner","doi":"10.1109/LICS.2012.30","DOIUrl":"https://doi.org/10.1109/LICS.2012.30","url":null,"abstract":"Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and parity objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two-player pushdown games. Finally we also show that all the problems have the same computational complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133891568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}