{"title":"Some Subsystems of Constant-Depth Frege with Parity","authors":"Michal Garlík, L. Kolodziejczyk","doi":"10.1145/3243126","DOIUrl":"https://doi.org/10.1145/3243126","url":null,"abstract":"We consider three relatively strong families of subsystems of AC0[2]-Frege proof systems, i.e., propositional proof systems using constant-depth formulas with an additional parity connective, for which exponential lower bounds on proof size are known. In order of increasing strength, the subsystems are (i) constant-depth proof systems with parity axioms and the (ii) treelike and (iii) daglike versions of systems introduced by Krajíček which we call PKcd(⊕). In a PKcd(⊕)-proof, lines are disjunctions (cedents) in which all disjuncts have depth at most d, parities can only appear as the outermost connectives of disjuncts, and all but c disjuncts contain no parity connective at all. We prove that treelike PKO(1)O(1)(⊕) is quasipolynomially but not polynomially equivalent to constant-depth systems with parity axioms. We also verify that the technique for separating parity axioms from parity connectives due to Impagliazzo and Segerlind can be adapted to give a superpolynomial separation between daglike PKO(1)O(1)(⊕) and AC0[2]-Frege; the technique is inherently unable to prove superquasipolynomial separations. We also study proof systems related to the system Res-Lin introduced by Itsykson and Sokolov. We prove that an extension of treelike Res-Lin is polynomially simulated by a system related to daglike PKO(1)O(1)(⊕), and obtain an exponential lower bound for this system.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126869371","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 Simple Modal Logic for Reasoning in Multigranulation Rough Set Model","authors":"Md. Aquil Khan, V. S. Patel","doi":"10.1145/3274664","DOIUrl":"https://doi.org/10.1145/3274664","url":null,"abstract":"The notions of strong/weak approximations have been studied extensively in recent years. These approximations are based on a structure of the form (W,{Ri}i∈ N), called the multiple-source approximation system, where Ri is an equivalence relation on W, and N is an initial segment of the set N of natural numbers. We propose and explore a simple modal language and semantics that can be used to reason about the strong/weak approximations of concepts. Moreover, our study is not confined to collections of equivalence relations only, but other types of relations are also considered. This study is important, keeping in view the notions of generalized approximation spaces with relations other than equivalence.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"2009 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127336238","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":"Automated Equivalence Checking of Concurrent Quantum Systems","authors":"Ebrahim Ardeshir-Larijani, S. Gay, R. Nagarajan","doi":"10.1145/3231597","DOIUrl":"https://doi.org/10.1145/3231597","url":null,"abstract":"The novel field of quantum computation and quantum information has gathered significant momentum in the last few years. It has the potential to radically impact the future of information technology and influence the development of modern society. The construction of practical, general purpose quantum computers has been challenging, but quantum cryptographic and communication devices have been available in the commercial marketplace for several years. Quantum networks have been built in various cities around the world and a dedicated satellite has been launched by China to provide secure quantum communication. Such new technologies demand rigorous analysis and verification before they can be trusted in safety- and security-critical applications. Experience with classical hardware and software systems has shown the difficulty of achieving robust and reliable implementations. We present CCSq, a concurrent language for describing quantum systems, and develop verification techniques for checking equivalence between CCSq processes. CCSq has well-defined operational and superoperator semantics for protocols that are functional, in the sense of computing a deterministic input-output relation for all interleavings arising from concurrency in the system. We have implemented QEC (Quantum Equivalence Checker), a tool that takes the specification and implementation of quantum protocols, described in CCSq, and automatically checks their equivalence. QEC is the first fully automatic equivalence checking tool for concurrent quantum systems. For efficiency purposes, we restrict ourselves to Clifford operators in the stabilizer formalism, but we are able to verify protocols over all input states. We have specified and verified a collection of interesting and practical quantum protocols, ranging from quantum communication and quantum cryptography to quantum error correction.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126589111","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}
E. Albert, J. Correas, E. Johnsen, Ka I Pun, G. Román-Díez
{"title":"Parallel Cost Analysis","authors":"E. Albert, J. Correas, E. Johnsen, Ka I Pun, G. Román-Díez","doi":"10.1145/3274278","DOIUrl":"https://doi.org/10.1145/3274278","url":null,"abstract":"This article presents parallel cost analysis, a static cost analysis targeting to over-approximate the cost of parallel execution in distributed systems. In contrast to the standard notion of serial cost, parallel cost captures the cost of synchronized tasks executing in parallel by exploiting the true concurrency available in the execution model of distributed processing. True concurrency is challenging for static cost analysis, because the parallelism between tasks needs to be soundly inferred, and the waiting and idle processor times at the different locations need to be accounted for. Parallel cost analysis works in three phases: (1) it performs a block-level analysis to estimate the serial costs of the blocks between synchronization points in the program; (2) it then constructs a distributed flow graph (DFG) to capture the parallelism, the waiting, and idle times at the locations of the distributed system; and (3) the parallel cost can finally be obtained as the path of maximal cost in the DFG. We prove the correctness of the proposed parallel cost analysis, and provide a prototype implementation to perform an experimental evaluation of the accuracy and feasibility of the proposed analysis.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122665341","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":"1-Safe Petri Nets and Special Cube Complexes","authors":"Jérémie Chalopin, V. Chepoi","doi":"10.1145/3322095","DOIUrl":"https://doi.org/10.1145/3322095","url":null,"abstract":"Nielsen et al. [35] proved that every 1-safe Petri net N unfolds into an event structure EN. By a result of Thiagarajan [46], these unfoldings are exactly the trace-regular event structures. Thiagarajan [46] conjectured that regular event structures correspond exactly to trace-regular event structures. In a recent paper (Chalopin and Chepoi [12]), we disproved this conjecture, based on the striking bijection between domains of event structures, median graphs, and CAT(0) cube complexes. However, we proved that Thiagarajan’s conjecture is true for regular event structures whose domains are principal filters of universal covers of finite special cube complexes. In the current article, we prove the converse: To any finite 1-safe Petri net N, one can associate a finite special cube complex XN such that the domain of the event structure EN (obtained as the unfolding of N) is a principal filter of the universal cover X̃N of XN. This establishes a bijection between 1-safe Petri nets and finite special cube complexes and provides a combinatorial characterization of trace-regular event structures. Using this bijection and techniques from graph theory and geometry (MSO theory of graphs, bounded treewidth, and bounded hyperbolicity), we disprove yet another conjecture by Thiagarajan (from the paper with Yang [48]) that the monadic second-order logic of a 1-safe Petri net (i.e., of its event structure unfolding) is decidable if and only if its unfolding is grid-free. It was proven by Thiagarajan and Yang [48] that the MSO logic is undecidable if the unfolding is not grid-free. Our counterexample is the trace-regular event structure that arises from a virtually special square complex Z. The domain of this event structure ĖZ is the principal filter of the universal cover Z̃ of Z in which to each vertex we added a pendant edge. The graph of the domain of ĖZ has bounded hyperbolicity (and, thus, the event structure ĖZ is grid-free) but has infinite treewidth. Using results of Seese, Courcelle, and Müller and Schupp, we show that this implies that the MSO theory of the event structure ĖZ is undecidable.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125060343","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}
Jakub Gajarský, S. Kreutzer, J. Nesetril, P. D. Mendez, Michal Pilipczuk, S. Siebertz, Szymon Toruńczyk
{"title":"First-Order Interpretations of Bounded Expansion Classes","authors":"Jakub Gajarský, S. Kreutzer, J. Nesetril, P. D. Mendez, Michal Pilipczuk, S. Siebertz, Szymon Toruńczyk","doi":"10.1145/3382093","DOIUrl":"https://doi.org/10.1145/3382093","url":null,"abstract":"The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order transductions of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low treedepth covers (or colorings), replacing treedepth by its dense analogue called shrubdepth.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130849182","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}
Facundo Carreiro, Alessandro Facchini, Y. Venema, F. Zanasi
{"title":"The Power of the Weak","authors":"Facundo Carreiro, Alessandro Facchini, Y. Venema, F. Zanasi","doi":"10.1145/3372392","DOIUrl":"https://doi.org/10.1145/3372392","url":null,"abstract":"A landmark result in the study of logics for formal verification is Janin and Walukiewicz’s theorem, stating that the modal μ-calculus (μML) is equivalent modulo bisimilarity to standard monadic second-order logic (here abbreviated as SMSO) over the class of labelled transition systems (LTSs for short). Our work proves two results of the same kind, one for the alternation-free or noetherian fragment μNML of μML on the modal side and one for WMSO, weak monadic second-order logic, on the second-order side. In the setting of binary trees, with explicit functions accessing the left and right successor of a node, it was known that WMSO is equivalent to the appropriate version of alternation-free μ-calculus. Our analysis shows that the picture changes radically once we consider, as Janin and Walukiewicz did, the standard modal μ-calculus, interpreted over arbitrary LTSs. The first theorem that we prove is that, over LTSs, μNML is equivalent modulo bisimilarity to noetherian MSO (NMSO), a newly introduced variant of SMSO where second-order quantification ranges over “conversely well-founded” subsets only. Our second theorem starts from WMSO and proves it equivalent modulo bisimilarity to a fragment of μNML defined by a notion of continuity. Analogously to Janin and Walukiewicz’s result, our proofs are automata-theoretic in nature: As another contribution, we introduce classes of parity automata characterising the expressiveness of WMSO and NMSO (on tree models) and of μCML and μNML (for all transition systems).","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"50 14","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113937052","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":"Relating Paths in Transition Systems","authors":"C. Dima, Bastien Maubert, S. Pinchinat","doi":"10.1145/3231596","DOIUrl":"https://doi.org/10.1145/3231596","url":null,"abstract":"We revisit Janin and Walukiewicz’s classic result on the expressive completeness of the modal mu-calculus with respect to Monadic Second Order Logic (MSO), which is where the mu-calculus corresponds precisely to the fragment of MSO that is invariant under bisimulation. We show that adding binary relations over finite paths in the picture may alter the situation. We consider a general setting where finite paths of transition systems are linked by means of a fixed binary relation. This setting gives rise to natural extensions of MSO and the mu-calculus, that we call the MSO with paths relation and the jumping mu-calculus, the expressivities of which we aim at comparing. We first show that “bounded-memory” binary relations bring about no additional expressivity to either of the two logics, and thus preserve expressive completeness. In contrast, we show that for a natural, classic “infinite-memory” binary relation stemming from games with imperfect information, the existence of a winning strategy in such games, though expressible in the bisimulation-invariant fragment of MSO with paths relation, cannot be expressed in the jumping mu-calculus. Expressive completeness thus fails for this relation. These results crucially rely on our observation that the jumping mu-calculus has a tree automata counterpart: the jumping tree automata, hence the name of the jumping mu-calculus. We also prove that for observable winning conditions, the existence of winning strategies in games with imperfect information is expressible in the jumping mu-calculus. Finally, we derive from our main theorem that jumping automata cannot be projected, and ATL with imperfect information does not admit expansion laws.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127598083","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":"Automated Deduction in Gödel Logic","authors":"Dušan Guller","doi":"10.1145/3218817","DOIUrl":"https://doi.org/10.1145/3218817","url":null,"abstract":"This article addresses the deduction problem of a formula from a countable theory in the first-order Gödel logic. We generalise the well-known hyperresolution principle for deduction in Gödel logic. Our approach is based on translation of a formula to an equivalent satisfiable finite order clausal theory, consisting of order clauses. We introduce a notion of quantified atom: a formula a is a quantified atom if a = Qx, p(t0, …, tn), where Q is a quantifier (∀, ∃), p(t0, …, tn) is an atom, and x is a variable occurring in p(t0, …, tn); for all i ≤ n, either ti = x or x does not occur in ti. Then an order clause is a finite set of order literals of the form ϵ1 ⋄ ϵ 2, where ϵi is either an atom, or a truth constant (0, 1), or a quantified atom, and ⋄ is either a connective ≖, equality, or ≺ strict order. ≖ and ≺ are interpreted by the equality and standard strict linear order on [0, 1], respectively. On the basis of the hyperresolution principle, a calculus operating over order clausal theories is devised. The calculus is proved to be refutation sound and complete for the countable case. As an interesting consequence, we get an affirmative solution to the open problem of recursive enumerability of unsatisfiable formulae in Gödel logic.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134356613","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}
A. Cimatti, A. Griggio, A. Irfan, M. Roveri, R. Sebastiani
{"title":"Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions","authors":"A. Cimatti, A. Griggio, A. Irfan, M. Roveri, R. Sebastiani","doi":"10.1145/3230639","DOIUrl":"https://doi.org/10.1145/3230639","url":null,"abstract":"Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some theory or combination of theories; Verification Modulo Theories (VMT) is the problem of analyzing the reachability for transition systems represented in terms of SMT formulae. In this article, we tackle the problems of SMT and VMT over the theories of nonlinear arithmetic over the reals (NRA) and of NRA augmented with transcendental (exponential and trigonometric) functions (NTA). We propose a new abstraction-refinement approach for SMT and VMT on NRA or NTA, called Incremental Linearization. The idea is to abstract nonlinear multiplication and transcendental functions as uninterpreted functions in an abstract space limited to linear arithmetic on the rationals with uninterpreted functions. The uninterpreted functions are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear constraints. In the case of transcendental functions, particular care is required to ensure the soundness of the abstraction. The method has been implemented in the MathSAT SMT solver and in the nuXmv model checker. An extensive experimental evaluation on a wide set of benchmarks from verification and mathematics demonstrates the generality and the effectiveness of our approach.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125708494","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}
京公网安备 11010802042870号
求助内容：
应助结果提醒方式：