ACM Transactions on Computational Logic (TOCL)最新文献

{"title":"Algorithmic Compression of Finite Tree Languages by Rigid Acyclic Grammars","authors":"Sebastian Eberhard, Gabriel Ebner, Stefan Hetzl","doi":"10.1145/3127401","DOIUrl":"https://doi.org/10.1145/3127401","url":null,"abstract":"We present an algorithm to optimally compress a finite set of terms using a vectorial totally rigid acyclic tree grammar. This class of grammars has a tight connection to proof theory, and the grammar compression problem considered in this article has applications in automated deduction. The algorithm is based on a polynomial-time reduction to the MaxSAT optimization problem. The crucial step necessary to justify this reduction consists of applying a term rewriting relation to vectorial totally rigid acyclic tree grammars. Our implementation of this algorithm performs well on a large real-world dataset.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122504018","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":"On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances","authors":"Ronald de Haan, Iyad A. Kanj, Stefan Szeider","doi":"10.1145/3091528","DOIUrl":"https://doi.org/10.1145/3091528","url":null,"abstract":"In many practical settings it is useful to find a small unsatisfiable subset of a given unsatisfiable set of constraints. We study this problem from a parameterized complexity perspective, taking the size of the unsatisfiable subset as the natural parameter where the set of constraints is either (i) given a set of clauses, i.e., a formula in conjunctive normal Form (CNF), or (ii) as an instance of the Constraint Satisfaction Problem (CSP). In general, the problem is fixed-parameter intractable. For an instance of the propositional satisfiability problem (SAT), it was known to be W[1]-complete. We establish A[2]-completeness for CSP instances, where A[2]-hardness prevails already for the Boolean case. With these fixed-parameter intractability results for the general case in mind, we consider various restricted classes of inputs and draw a detailed complexity landscape. It turns out that often Boolean CSP and CNF formulas behave similarly, but we also identify notable exceptions to this rule. The main part of this article is dedicated to classes of inputs that are induced by Boolean constraint languages that Schaefer [1978] identified as the maximal constraint languages with a tractable satisfiability problem. We show that for the CSP setting, the problem of finding small unsatisfiable subsets remains fixed-parameter intractable for all Schaefer languages for which the problem is non-trivial. We show that this is also the case for CNF formulas with the exception of the class of bijunctive (Krom) formulas, which allows for an identification of a small unsatisfiable subset in polynomial time. In addition, we consider various restricted classes of inputs with bounds on the maximum number of times that a variable occurs (the degree), bounds on the arity of constraints, and bounds on the domain size. For the case of CNF formulas, we show that restricting the degree is enough to obtain fixed-parameter tractability, whereas for the case of CSP instances, one needs to restrict the degree, the arity, and the domain size simultaneously to establish fixed-parameter tractability. Finally, we relate the problem of finding small unsatisfiable subsets of a set of constraints to the problem of identifying whether a given variable-value assignment is entailed or forbidden already by a small subset of constraints. Moreover, we use the connection between the two problems to establish similar parameterized complexity results also for the latter problem.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130541534","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":"The Logical View on Continuous Petri Nets","authors":"Michael Blondin, A. Finkel, C. Haase, S. Haddad","doi":"10.1145/3105908","DOIUrl":"https://doi.org/10.1145/3105908","url":null,"abstract":"Continuous Petri nets are a relaxation of classical discrete Petri nets in which transitions can be fired a fractional number of times, and consequently places may contain a fractional number of tokens. Such continuous Petri nets are an appealing object to study, since they over-approximate the set of reachable configurations of their discrete counterparts, and their reachability problem is known to be decidable in polynomial time. The starting point of this article is to show that the reachability relation for continuous Petri nets is definable by a sentence of linear size in the existential theory of the rationals with addition and order. Using this characterization, we obtain decidability and complexity results for a number of classical decision problems for continuous Petri nets. In particular, we settle the open problem about the precise complexity of reachability set inclusion. Finally, we show how continuous Petri nets can be incorporated inside the classical backward coverability algorithm for discrete Petri nets as a pruning heuristic to tackle the symbolic state explosion problem. The cornerstone of the approach we present is that our logical characterization enables us to leverage the power of modern SMT-solvers to yield a highly performant and robust decision procedure for coverability in Petri nets. We demonstrate the applicability of our approach on a set of standard benchmarks from the literature.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122524047","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":"An O(mlogn) Algorithm for Computing Stuttering Equivalence and Branching Bisimulation","authors":"J. F. Groote, D. Jansen, J. Keiren, Anton Wijs","doi":"10.1145/3060140","DOIUrl":"https://doi.org/10.1145/3060140","url":null,"abstract":"We provide a new algorithm to determine stuttering equivalence with time complexity O(mlogn), where n is the number of states and m is the number of transitions of a Kripke structure. This algorithm can also be used to determine branching bisimulation in O(m(log |Act| + log n)) time, where Act is the set of actions in a labeled transition system. Theoretically, our algorithm substantially improves upon existing algorithms, which all have time complexity of the form O(mn) at best. Moreover, it has better or equal space complexity. Practical results confirm these findings: they show that our algorithm can outperform existing algorithms by several orders of magnitude, especially when the Kripke structures are large. The importance of our algorithm stretches far beyond stuttering equivalence and branching bisimulation. The known O(mn) algorithms were already far more efficient (both in space and time) than most other algorithms to determine behavioral equivalences (including weak bisimulation), and therefore they were often used as an essential preprocessing step. This new algorithm makes this use of stuttering equivalence and branching bisimulation even more attractive.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124953386","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":"Possibilistic Justification Logic","authors":"Che-Ping Su, T. Fan, C. Liau","doi":"10.1145/3091118","DOIUrl":"https://doi.org/10.1145/3091118","url":null,"abstract":"Justification logic originated from the study of the logic of proofs. However, in a more general setting, it may be regarded as a kind of explicit epistemic logic. In such logic, the reasons a fact is believed are explicitly represented as justification terms. Traditionally, the modeling of uncertain beliefs is crucially important for epistemic reasoning. Graded modal logics interpreted with possibility theory semantics have been successfully applied to the representation and reasoning of uncertain beliefs; however, they cannot keep track of the reasons an agent believes a fact. This article is aimed at extending the graded modal logics with explicit justifications. We introduce a possibilistic justification logic, present its syntax and semantics, and investigate its metaproperties, such as soundness, completeness, and realizability.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127227346","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":"The NP Search Problems of Frege and Extended Frege Proofs","authors":"A. Beckmann, S. Buss","doi":"10.1145/3060145","DOIUrl":"https://doi.org/10.1145/3060145","url":null,"abstract":"We study consistency search problems for Frege and extended Frege proofs—namely the NP search problems of finding syntactic errors in Frege and extended Frege proofs of contradictions. The input is a polynomial time function, or an oracle, describing a proof of a contradiction; the output is the location of a syntactic error in the proof. The consistency search problems for Frege and extended Frege systems are shown to be many-one complete for the provably total NP search problems of the second-order bounded arithmetic theories U12 and V12, respectively.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125642614","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":"Progression of Decomposed Local-Effect Action Theories","authors":"D. Ponomaryov, M. Soutchanski","doi":"10.1145/3091119","DOIUrl":"https://doi.org/10.1145/3091119","url":null,"abstract":"In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of weakly related or independent components. However, a theory may represent knowledge that is subject to change, as a result of executing actions that have effects on some of the initial properties mentioned in the theory. Having once computed a decomposition of a theory, it is advantageous to know whether a decomposition has to be computed again in the newly changed theory (obtained from taking into account changes resulting from execution of an action). In this article, we address this problem in the scope of the situation calculus, where a change of an initial theory is related to the notion of progression. Progression provides a form of forward reasoning; it relies on forgetting values of those properties, which are subject to change, and computing new values for them. We consider decomposability and inseparability, two component properties known from the literature, and contribute by studying the conditions (1) when these properties are preserved and (2) when they are lost wrt progression and the related operation of forgetting. To show the latter, we demonstrate the boundaries using a number of negative examples. To show the former, we identify cases when these properties are preserved under forgetting and progression of initial theories in local-effect basic action theories of the situation calculus. Our article contributes to bridging two different communities in knowledge representation, namely, research on modularity and research on reasoning about actions.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131870631","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 Generation of Erotetic Search Scenarios","authors":"Szymon Chlebowski, Maciej Komosinski, A. Kups","doi":"10.1145/3056537","DOIUrl":"https://doi.org/10.1145/3056537","url":null,"abstract":"This article concerns automated generation and processing of erotetic search scenarios (ESSs). ESSs are formal constructs characterized in Inferential Erotetic Logic that enable finding possible answers to a posed question by decomposing it into auxiliary questions. The first part of this work describes a formal account on ESSs. The formal approach is then applied to automatically generate ESSs, and the resulting scenarios are evaluated according to a number of criteria. These criteria are subjected to discordance analysis that reveals their mutual relationships. Finally, knowledge concerning relationships between different values of evaluation criteria is extracted by applying Apriori—an association rules mining algorithm. The proposed approach of integration of formal erotetic logic with computational tools provides extensive insight into the former and helps with the development of efficient ESSs.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126149717","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":"Quantified Constraint Satisfaction Problem on Semicomplete Digraphs","authors":"Petar Đapić, P. Marković, B. Martin","doi":"10.1145/3007899","DOIUrl":"https://doi.org/10.1145/3007899","url":null,"abstract":"We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over semicomplete digraphs. We obtain a complexity-theoretic trichotomy: QCSP(H) is either in P, is NP-complete, or is Pspace-complete. The largest part of our work is the algebraic classification of precisely which semicomplete digraphs enjoy only essentially unary polymorphisms, which is combinatorially interesting in its own right.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132188793","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":"Subatomic Proof Systems","authors":"Andrea Aler Tubella, Alessio Guglielmi","doi":"10.1145/3173544","DOIUrl":"https://doi.org/10.1145/3173544","url":null,"abstract":"This article presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalization, and in particular of cut elimination. By considering atoms as self-dual noncommutative connectives, we are able to classify a vast class of inference rules in a uniform and very simple way. This allows us to define simple conditions that are easily verifiable and that ensure normalization and cut elimination by way of a general theorem. In this article, we define and consider splittable systems, which essentially make up a large class of linear logics, including Multiplicative Linear Logic and BV, and we prove for them a splitting theorem, guaranteeing cut elimination and other admissibility results as corollaries. In articles to follow, we will extend this result to nonlinear logics. The final outcome will be a comprehensive theory giving a uniform treatment for most existing logics and providing a blueprint for the design of future proof systems.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126882608","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}