Lorenzo Clemente, S. Lasota, R. Lazic, Filip Mazowiecki
{"title":"Binary Reachability of Timed-register Pushdown Automata and Branching Vector Addition Systems","authors":"Lorenzo Clemente, S. Lasota, R. Lazic, Filip Mazowiecki","doi":"10.1145/3326161","DOIUrl":"https://doi.org/10.1145/3326161","url":null,"abstract":"Timed-register pushdown automata constitute a very expressive class of automata, whose transitions may involve state, input, and top-of-stack timed registers with unbounded differences. They strictly subsume pushdown timed automata of Bouajjani et al., dense-timed pushdown automata of Abdulla et al., and orbit-finite timed-register pushdown automata of Clemente and Lasota. We give an effective logical characterisation of the reachability relation of timed-register pushdown automata. As a corollary, we obtain a doubly exponential time procedure for the non-emptiness problem. We show that the complexity reduces to singly exponential under the assumption of monotonic time. The proofs involve a novel model of one-dimensional integer branching vector addition systems with states. As a result interesting on its own, we show that reachability sets of the latter model are semilinear and computable in exponential time.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114524431","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":"Pure Sequent Calculi","authors":"O. Lahav, Yoni Zohar","doi":"10.1145/3319501","DOIUrl":"https://doi.org/10.1145/3319501","url":null,"abstract":"Analyticity, also known as the subformula property, typically guarantees decidability of derivability in propositional sequent calculi. To utilize this fact, two substantial gaps have to be addressed: (i) What makes a sequent calculus analytic? and (ii) How do we obtain an efficient decision procedure for derivability in an analytic calculus? In the first part of this article, we answer these questions for pure calculi—a general family of fully structural propositional sequent calculi whose rules allow arbitrary context formulas. We provide a sufficient syntactic criterion for analyticity in these calculi, as well as a productive method to construct new analytic calculi from given ones. We further introduce a scalable decision procedure for derivability in analytic pure calculi by showing that it can be (uniformly) reduced to classical satisfiability. In the second part of the article, we study the extension of pure sequent calculi with modal operators. We show that such extensions preserve the analyticity of the calculus and identify certain restricted operators (which we call “Next” operators) that are also amenable for a general reduction of derivability to classical satisfiability. Our proofs are all semantic, utilizing several strong general soundness and completeness theorems with respect to non-deterministic semantic frameworks: bivaluations (for pure calculi) and Kripke models (for their extension with modal operators).","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130445746","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":"Fast Query Answering over Existential Rules","authors":"N. Leone, M. Manna, G. Terracina, P. Veltri","doi":"10.1145/3308448","DOIUrl":"https://doi.org/10.1145/3308448","url":null,"abstract":"Enhancing Datalog with existential quantification gives rise to Datalog∃, a powerful knowledge representation language widely used in ontology-based query answering. In this setting, a conjunctive query is evaluated over a Datalog∃ program consisting of extensional data paired with so-called “existential” rules. Owing to their high expressiveness, such rules make the evaluation of queries undecidable, even when the latter are atomic. Decidable generalizations of Datalog by existential rules have been proposed in the literature (such as weakly acyclic and weakly guarded); but they pay the price of higher computational complexity, hindering the implementation of effective systems. Conversely, the results in this article demonstrate that it is definitely possible to enable fast yet powerful query answering over existential rules that strictly generalize Datalog by ensuring decidability without any complexity overhead. On the theoretical side, we define the class of parsimonious programs that guarantees decidability of atomic queries. We then strengthen this class to strongly parsimonious programs ensuring decidability also for conjunctive queries. Since parsimony is an undecidable property, we single out Shy, an easily recognizable class of strongly parsimonious programs that generalizes Datalog while preserving its complexity even under conjunctive queries. Shy also generalizes the class of linear existential programs, while it is uncomparable to the other main classes ensuring decidability. On the practical side, we exploit our results to implement DLV∃, an effective system for query answering over parsimonious existential rules. To assess its efficiency, we carry out an experimental analysis, evaluating DLV∃ performances for ontology-based query answering on both real-world and synthetic ontologies.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129049751","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":"Reasoning about Strategic Abilities","authors":"N. Bulling, W. Jamroga, Matei Popovici","doi":"10.1145/3309761","DOIUrl":"https://doi.org/10.1145/3309761","url":null,"abstract":"In alternating-time temporal logic ATL*, agents with perfect recall assign choices to sequences of states, i.e., to possible finite histories of the game. However, when a nested strategic modality is interpreted, the new strategy does not take into account the previous sequence of events. It is as if agents collect their observations in the nested game again from scratch, thus, effectively forgetting what they observed before. Intuitively, it does not fit the assumption of agents having perfect recall of the past. In this article, we investigate the alternative semantics for ATL* where the past is not forgotten in nested games. We show that the standard semantics of ATL* coincides with the “truly perfect recall” semantics for agents with perfect information and in case of so-called “objective” abilities under uncertainty. On the other hand, the two semantics differ significantly for the most popular (“subjective”) notion of ability under imperfect information. The same applies to the standard vs. “truly perfect recall” semantics of ATL* with persistent strategies. We compare the relevant variants of ATL* by looking at their expressive power, sets of validities, and tractability of model checking.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125337872","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 First-order Logic for Reasoning about Knowledge and Probability","authors":"Sinisa Tomovic, Z. Ognjanovic, Dragan Doder","doi":"10.1145/3359752","DOIUrl":"https://doi.org/10.1145/3359752","url":null,"abstract":"We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. We define its syntax and semantics and prove the strong completeness property of the corresponding axiomatic system.1","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129071614","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 Theoretical and Numerical Analysis of the Worst-Case Size of Reduced Ordered Binary Decision Diagrams","authors":"Jim E. Newton, D. Verna","doi":"10.1145/3274279","DOIUrl":"https://doi.org/10.1145/3274279","url":null,"abstract":"Binary Decision Diagrams (BDDs) and in particular ROBDDs (Reduced Ordered BDDs) are a common data structure for manipulating Boolean expressions, integrated circuit design, type inferencers, model checkers, and many other applications. Although the ROBDD is a lightweight data structure to implement, the behavior, in terms of memory allocation, may not be obvious to the program architect. We explore experimentally, numerically, and theoretically the typical and worst-case ROBDD sizes in terms of number of nodes and residual compression ratios, as compared to unreduced BDDs. While our theoretical results are not surprising, as they are in keeping with previously known results, we believe our method contributes to the current body of research by our experimental and statistical treatment of ROBDD sizes. In addition, we provide an algorithm to calculate the worst-case size. Finally, we present an algorithm for constructing a worst-case ROBDD of a given number of variables. Our approach may be useful to projects deciding whether the ROBDD is the appropriate data structure to use, and in building worst-case examples to test their code.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"211 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115827265","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":"Generalized Eilenberg Theorem","authors":"J. Adámek, Stefan Milius, R. Myers, Henning Urbat","doi":"10.1145/3276771","DOIUrl":"https://doi.org/10.1145/3276771","url":null,"abstract":"For finite automata as coalgebras in a category C, we study languages they accept and varieties of such languages. This generalizes Eilenberg’s concept of a variety of languages, which corresponds to choosing as C the category of Boolean algebras. Eilenberg established a bijective correspondence between pseudovarieties of monoids and varieties of regular languages. In our generalization, we work with a pair C/D of locally finite varieties of algebras that are predual, i.e., dualize on the level of finite algebras, and we prove that pseudovarieties of D-monoids bijectively correspond to varieties of regular languages in C. As one instance, Eilenberg’s result is recovered by choosing D = sets and C = Boolean algebras. Another instance, Pin’s result on pseudovarieties of ordered monoids, is covered by taking D = posets and C = distributive lattices. By choosing as C amp;equals; D the self-predual category of join-semilattices, we obtain Polák’s result on pseudovarieties of idempotent semirings. Similarly, using the self-preduality of vector spaces over a finite field K, our result covers that of Reutenauer on pseudovarieties of K-algebras. Several new variants of Eilenberg’s theorem arise by taking other predualities, e.g., between the categories of non-unital Boolean rings and of pointed sets. In each of these cases, we also prove a local variant of the bijection, where a fixed alphabet is assumed and one considers local varieties of regular languages over that alphabet in the category C.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116968184","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}
Kord Eickmeyer, J. V. D. Heuvel, K. Kawarabayashi, S. Kreutzer, P. D. Mendez, Michal Pilipczuk, D. Quiroz, Roman Rabinovich, S. Siebertz
{"title":"Model-Checking on Ordered Structures","authors":"Kord Eickmeyer, J. V. D. Heuvel, K. Kawarabayashi, S. Kreutzer, P. D. Mendez, Michal Pilipczuk, D. Quiroz, Roman Rabinovich, S. Siebertz","doi":"10.1145/3360011","DOIUrl":"https://doi.org/10.1145/3360011","url":null,"abstract":"We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but it does become tractable on interesting classes of structures, such as on classes whose Gaifman graphs have bounded treewidth. In this article, we continue this line of research and study model-checking for first- and monadic second-order logic in the presence of an ordering on the input structure. We do so in two settings: the general ordered case, where the input structures are equipped with a fixed order or successor relation, and the order-invariant case, where the formulas may resort to an ordering, but their truth must be independent of the particular choice of order. In the first setting we show very strong intractability results for most interesting classes of structures. In contrast, in the order-invariant case we obtain tractability results for order-invariant monadic second-order formulas on the same classes of graphs as in the unordered case. For first-order logic, we obtain tractability of successor-invariant formulas on classes whose Gaifman graphs have bounded expansion. Furthermore, we show that model-checking for order-invariant first-order formulas is tractable on coloured posets of bounded width.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"233 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123277224","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 Modular Type Reconstruction Algorithm","authors":"Florian Rabe","doi":"10.1145/3234693","DOIUrl":"https://doi.org/10.1145/3234693","url":null,"abstract":"Mmt is a framework for designing and implementing formal systems in a way that systematically abstracts from theoretical and practical aspects of their type of theoretical and logical foundations. Thus, definitions, theorems, and algorithms can be stated independently of the foundation, and language designers can focus on the essentials of a particular foundation and inherit a large-scale implementation from Mmt at low cost. Going beyond the similarly motivated approach of meta-logical frameworks, Mmt does not even commit to a particular meta-logic—that makes Mmt level results harder to obtain but also more general. We present one such result: a type reconstruction algorithm that realizes the foundation-independent aspects generically relative to a set of rules that supply the foundation-specific knowledge. Maybe surprisingly, we see that the former covers most of the algorithm, including the most difficult details. Thus, we can easily instantiate our algorithm with rule sets for several important language features including, e.g., dependent function types. Moreover, our design is modular such that we obtain a type reconstruction algorithm for any combination of these features.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125804368","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}
Yongjian Li, Kaiqiang Duan, D. Jansen, Jun Pang, Lijun Zhang, Yi Lv, Shaowei Cai
{"title":"An Automatic Proving Approach to Parameterized Verification","authors":"Yongjian Li, Kaiqiang Duan, D. Jansen, Jun Pang, Lijun Zhang, Yi Lv, Shaowei Cai","doi":"10.1145/3232164","DOIUrl":"https://doi.org/10.1145/3232164","url":null,"abstract":"Formal verification of parameterized protocols such as cache coherence protocols is a significant challenge. In this article, we propose an automatic proving approach and its prototype paraVerifier to handle this challenge within a unified framework as follows: (1) To prove the correctness of a parameterized protocol, our approach automatically discovers auxiliary invariants and the corresponding dependency relations among the discovered invariants and protocol rules from a small instance of the to-be-verified protocol, and (2) the discovered invariants and dependency graph are then automatically generalized into a parameterized form and sent to the theorem prover, Isabelle. As a side product, the final verification result of a protocol is provided by a formal and human-readable proof. Our approach has been successfully applied to a number of benchmarks, including snoopying-based and directory-based cache coherence protocols.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122198236","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}
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