ACM Transactions on Computational Logic (TOCL)最新文献

{"title":"Finite-State Map-Reduce Computation and Relational Algebra Queries","authors":"F. Neven, Nicole Schweikardt, Frédéric Servais, Tony Tan","doi":"10.1145/3197384","DOIUrl":"https://doi.org/10.1145/3197384","url":null,"abstract":"We introduce three formal models of distributed systems for query evaluation on massive databases: Distributed Streaming with Register Automata (DSAs), Distributed Streaming with Register Transducers (DSTs), and Distributed Streaming with Register Transducers and Joins (DSTJs). These models are based on the map-reduce paradigm where the input is transformed into a dataset of key-value pairs, and on each key a local computation is performed on the values associated with that key resulting in another set of key-value pairs. Computation proceeds in a constant number of rounds, where the result of the last round is the input to the next round, and transformation of key-value pairs is required to be generic. The difference between the three models is in the local computation part. In DSAs it is limited to making one pass over its input using a register automaton, while in DSTs it can make two passes: in the first pass it uses a finite state automaton and in the second it uses a register transducer. The third model DSTJs is an extension of DSTs, where local computations are capable of constructing the Cartesian product of two sets. We obtain the following results: (1) DSAs can evaluate first-order queries over bounded degree databases; (2) DSTs can evaluate semijoin algebra queries over arbitrary databases; (3) DSTJs can evaluate the whole relational algebra over arbitrary databases; (4) DSTJs are strictly stronger than DSTs, which in turn are strictly stronger than DSAs; (5) within DSAs, DSTs, and DSTJs, there is a strict hierarchy w.r.t. the number of rounds.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126891922","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":"Compositional Synthesis of Piece-Wise Functions by Learning Classifiers","authors":"D. Neider, S. Saha, P. Madhusudan","doi":"10.1145/3173545","DOIUrl":"https://doi.org/10.1145/3173545","url":null,"abstract":"We present a novel general technique that uses classifier learning to synthesize piece-wise functions (functions that split the domain into regions and apply simpler functions to each region) against logical synthesis specifications. Our framework works by combining a synthesizer of functions for fixed concrete inputs and a synthesizer of predicates that can be used to define regions. We develop a theory of single-point refutable specifications that facilitate generating concrete counterexamples using constraint solvers. We implement the framework for synthesizing piece-wise functions in linear integer arithmetic, combining leaf expression synthesis using constraint-solving with predicate synthesis using enumeration, and tie them together using a decision tree classifier. We demonstrate that this compositional approach is competitive compared to existing synthesis engines on a set of synthesis specifications.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115621165","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":"Central Limit Model Checking","authors":"L. Bortolussi, L. Cardelli, M. Kwiatkowska, L. Laurenti","doi":"10.1145/3331452","DOIUrl":"https://doi.org/10.1145/3331452","url":null,"abstract":"We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical algorithms for CSL model checking based on uniformisation are limited to finite CTMCs and suffer from exponential growth of the state space with respect to the number of species. However, approximate techniques such as mean-field approximations and simulations combined with statistical inference are more scalable but can be time-consuming and do not support the full expressiveness of CSL. In this article, we employ a continuous-space approximation of the CTMC in terms of a Gaussian process based on the Central Limit Approximation, also known as the Linear Noise Approximation, whose solution requires solving a number of differential equations that is quadratic in the number of species and independent of the population size. We then develop efficient and scalable approximate model checking algorithms on the resulting Gaussian process, where we restrict the target regions for probabilistic reachability to convex polytopes. This allows us to derive an abstraction in terms of a time-inhomogeneous discrete-time Markov chain (DTMC), whose dimension is independent of the number of species, on which model checking is performed. Using results from probability theory, we prove the convergence in distribution of our algorithms to the corresponding measures on the original CTMC. We implement the techniques and, on a set of examples, demonstrate that they allow us to overcome the state space explosion problem, while still correctly characterizing the stochastic behaviour of the system. Our methods can be used for formal analysis of a wide range of distributed stochastic systems, including biochemical systems, sensor networks, and population protocols.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129135835","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":"Duality between Unprovability and Provability in Forward Refutation-search for Intuitionistic Propositional Logic","authors":"Camillo Fiorentini, Mauro Ferrari","doi":"10.1145/3372299","DOIUrl":"https://doi.org/10.1145/3372299","url":null,"abstract":"The inverse method is a saturation-based theorem-proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here, we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability, which is appropriate for constructively ascertaining the unprovability of a formula G by providing a concise countermodel for it; in particular, we prove that the generated countermodels have minimal height. Moreover, we clarify the role of the saturated database obtained as result of a failed proof-search in FRJ(G) by showing how to extract from such a database a derivation witnessing the Intuitionistic validity of the goal.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126862109","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":"Hypersequents and Systems of Rules","authors":"A. Ciabattoni, Francesco A. Genco","doi":"10.1145/3180075","DOIUrl":"https://doi.org/10.1145/3180075","url":null,"abstract":"We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of the benefits of locality for 2-systems, analyticity results for a large class of such systems, and a rewriting of hypersequent rules as natural deduction rules.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"183 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115061686","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":"O-Minimal Invariants for Discrete-Time Dynamical Systems","authors":"Shaull Almagor, D. Chistikov, J. Ouaknine, J. Worrell","doi":"10.1145/3501299","DOIUrl":"https://doi.org/10.1145/3501299","url":null,"abstract":"Termination analysis of linear loops plays a key rôle in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination relates to deep open problems in number theory, such as the decidability of the Skolem and Positivity Problems for linear recurrence sequences, or equivalently reachability questions for discrete-time linear dynamical systems. In this article, we introduce the class of o-minimal invariants, which is broader than any previously considered, and study the decidability of the existence and algorithmic synthesis of such invariants as certificates of non-termination for linear loops equipped with a large class of halting conditions. We establish two main decidability results, one of them conditional on Schanuel’s conjecture is transcendental number theory.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130542807","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":"Characterisation of Normalisation Properties for λμ using Strict Negated Intersection Types","authors":"S. V. Bakel","doi":"10.1145/3149823","DOIUrl":"https://doi.org/10.1145/3149823","url":null,"abstract":"We show characterisation results for normalisation, head-normalisation, and strong normalisation for λ μ using intersection types. We reach these results for a strict notion of type assignment for λ μ that is the natural restriction of the domain-based system of van Bakel et al. (2011) for λ μ by limiting the type inclusion relation to just intersection elimination. We show that this system respects β μ-equality, by showing both soundness and completeness results. We then define a notion of reduction on derivations that corresponds to cut-elimination, and show that this is strongly normalisable. We use this strong normalisation result to show an approximation result, and through that a characterisation of head-normalisation. Using the approximation result, we show that there is a very strong relation between the system of van Bakel et al. (2011) and ours. We then introduce a notion of type assignment that eliminates ω as an assignable type, and show, using the strong normalisation result for derivation reduction, that all terms typeable in this system are strongly normalisable as well, and show that all strongly normalisable terms are typeable. We conclude by adding type variables to our system, and show that system essentially is that of van Bakel (2010b).","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122436603","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":"Definability of Cai-Fürer-Immerman Problems in Choiceless Polynomial Time","authors":"Wied Pakusa, Svenja Schalthöfer, Erkal Selman","doi":"10.1145/3154456","DOIUrl":"https://doi.org/10.1145/3154456","url":null,"abstract":"Choiceless Polynomial Time (CPT) is one of the most promising candidates in the search for a logic capturing Ptime. The question whether there is a logic that expresses exactly the polynomial-time computable properties of finite structures, which has been open for more than 30 years, is one of the most important and challenging problems in finite model theory. The strength of Choiceless Polynomial Time is its ability to perform isomorphism-invariant computations over structures, using hereditarily finite sets as data structures. But, because of isomorphism-invariance, it is choiceless in the sense that it cannot select an arbitrary element of a set—an operation that is crucial for many classical algorithms. CPT can define many interesting Ptime queries, including (a certain version of) the Cai-Fürer-Immerman (CFI) query. The CFI-query is particularly interesting, because it separates fixed-point logic with counting from Ptime and has since remained the main benchmark for the expressibility of logics within Ptime. The CFI-construction associates with each connected graph a set of CFI-graphs that can be partitioned into exactly two isomorphism classes called odd and even CFI-graphs. The problem is to decide, given a CFI-graph, whether it is odd or even. For the case where the CFI-graphs arise from ordered graphs, Dawar, Richerby, and Rossman proved that the CFI-query is CPT-definable. However, definability of the CFI-query over general graphs remains open. Our first contribution generalises the result by Dawar, Richerby, and Rossman to the variant of the CFI-query derived from graphs with colour classes of logarithmic size, instead of colour class size one. Second, we consider the CFI-query over graph classes where the maximal degree is linear in the size of the graphs. For the latter, we establish CPT-definability using only sets of small, constant rank, which is known to be impossible for the general case. In our CFI-recognising procedures we strongly make use of the ability of CPT to create sets, rather than tuples only, and we further prove that, if CPT worked over tuples instead, then no such procedure would be definable. We introduce a notion of “sequencelike objects” based on the structure of the graphs’ symmetry groups, and we show that no CPT-program that only uses sequencelike objects can decide the CFI-query over complete graphs, which have linear maximal degree. From a broader perspective, this generalises a result by Blass, Gurevich, and van den Bussche about the power of isomorphism-invariant machine models (for polynomial time) to a setting with counting.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125316671","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":"Typed Nominal Rewriting","authors":"Elliot Fairweather, M. Fernández","doi":"10.1145/3161558","DOIUrl":"https://doi.org/10.1145/3161558","url":null,"abstract":"Nominal terms extend first-order terms with nominal features and as such constitute a meta-language for reasoning about the named variables of an object language in the presence of meta-level variables. This article introduces a number of type systems for nominal terms of increasing sophistication and demonstrates their application in the areas of rewriting and equational reasoning. Two simple type systems inspired by Church’s simply typed lambda calculus are presented where only well-typed terms are considered to exist, over which α-equivalence is then axiomatised. The first requires atoms to be strictly annotated whilst the second explores the consequences of a more relaxed de Bruijn-style approach in the presence of atom-capturing substitution. A final type system of richer ML-like polymorphic types is then given in the style of Curry, in which elements of the term language are deemed typeable or not only subsequent to the definition of alpha-equivalence. Principal types are shown to exist and an inference algorithm given to compute them. This system is then used to define two presentations of typed nominal rewriting, one more expressive and one more efficient, the latter also giving rise to a notion of typed nominal equational reasoning.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132021812","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":"Tight Bounds on the Asymptotic Descriptive Complexity of Subgraph Isomorphism","authors":"O. Verbitsky, M. Zhukovskii","doi":"10.1145/3303881","DOIUrl":"https://doi.org/10.1145/3303881","url":null,"abstract":"Let v(F) denote the number of vertices in a fixed connected pattern graph F. We show an infinite family of patterns F such that the existence of a subgraph isomorphic to F is expressible by a first-order sentence of quantifier depth 2/3 v(F) + 1, assuming that the host graph is sufficiently large and connected. However, this is impossible for any F using less than 2/3 v(F) - 2 first-order variables.","PeriodicalId":191685,"journal":{"name":"ACM Transactions on Computational Logic (TOCL)","volume":"38 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131935414","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}