Pub Date : 2021-01-01DOI: 10.1007/978-3-030-63777-4
R. Antonsen
{"title":"Logical Methods: The Art of Thinking Abstractly and Mathematically","authors":"R. Antonsen","doi":"10.1007/978-3-030-63777-4","DOIUrl":"https://doi.org/10.1007/978-3-030-63777-4","url":null,"abstract":"","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87990214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-03-04DOI: 10.2168/LMCS-10(2:2)2014
P. Hyvernat
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is reminiscent of Day's convolution on presheaves. We then make this category into a model for intuitionistic linear logic by defining an additive and exponential structure.
{"title":"A Linear Category of Polynomial Functors (extensional part)","authors":"P. Hyvernat","doi":"10.2168/LMCS-10(2:2)2014","DOIUrl":"https://doi.org/10.2168/LMCS-10(2:2)2014","url":null,"abstract":"We construct a symmetric monoidal closed category of polynomial endofunctors\u0000(as objects) and simulation cells (as morphisms). This structure is defined\u0000using universal properties without reference to representing polynomial\u0000diagrams and is reminiscent of Day's convolution on presheaves. We then make\u0000this category into a model for intuitionistic linear logic by defining an\u0000additive and exponential structure.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-08-01DOI: 10.2168/LMCS-10(3:24)2014
Thomas Place, L. V. Rooijen, M. Zeitoun
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting the input languages. We prove that the problem is computationally harder than deciding membership. The correctness proof of the algorithm yields a stronger result, namely a description of a possible separator. Finally, we discuss the same problem for context-free input languages.
{"title":"On Separation by Locally Testable and Locally Threshold Testable Languages","authors":"Thomas Place, L. V. Rooijen, M. Zeitoun","doi":"10.2168/LMCS-10(3:24)2014","DOIUrl":"https://doi.org/10.2168/LMCS-10(3:24)2014","url":null,"abstract":"A separator for two languages is a third language containing the first one\u0000and disjoint from the second one. We investigate the following decision\u0000problem: given two regular input languages, decide whether there exists a\u0000locally testable (resp. a locally threshold testable) separator. In both cases,\u0000we design a decision procedure based on the occurrence of special patterns in\u0000automata accepting the input languages. We prove that the problem is\u0000computationally harder than deciding membership. The correctness proof of the\u0000algorithm yields a stronger result, namely a description of a possible\u0000separator. Finally, we discuss the same problem for context-free input\u0000languages.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67823768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-02-02DOI: 10.2168/LMCS-11(4:6)2015
Stéphane Le Roux, A. Pauly
We investigate choice principles in the Weihrauch lattice for finite sets on the one hand, and convex sets on the other hand. Increasing cardinality and increasing dimension both correspond to increasing Weihrauch degrees. Moreover, we demonstrate that the dimension of convex sets can be characterized by the cardinality of finite sets encodable into them. Precisely, choice from an n + 1 point set is reducible to choice from a convex set of dimension n, but not reducible to choice from a convex set of dimension n–1. Furthermore we consider searching for zeros of continuous functions. We provide an algorithm producing 3n real numbers containing all zeros of a continuous function with up to n local minima. This demonstrates that having finitely many zeros is a strictly weaker condition than having finitely many local extrema. We can prove 3n to be optimal.
{"title":"Finite choice, convex choice and finding roots","authors":"Stéphane Le Roux, A. Pauly","doi":"10.2168/LMCS-11(4:6)2015","DOIUrl":"https://doi.org/10.2168/LMCS-11(4:6)2015","url":null,"abstract":"We investigate choice principles in the Weihrauch lattice for finite sets on the one hand, and convex sets on the other hand. Increasing cardinality and increasing dimension both correspond to increasing Weihrauch degrees. Moreover, we demonstrate that the dimension of convex sets can be characterized by the cardinality of finite sets encodable into them. Precisely, choice from an n + 1 point set is reducible to choice from a convex set of dimension n, but not reducible to choice from a convex set of dimension n–1. Furthermore we consider searching for zeros of continuous functions. We provide an algorithm producing 3n real numbers containing all zeros of a continuous function with up to n local minima. This demonstrates that having finitely many zeros is a strictly weaker condition than having finitely many local extrema. We can prove 3n to be optimal.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2013-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67823942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-03-29DOI: 10.2168/LMCS-8(1:32)2012
Isolde Adler, M. Weyer
We introduce tree-width for first order formulae phi, fotw(phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed parameter tractable, with parameter the length of the formula. This is done by translating a formula phi with fotw(phi)
{"title":"Tree-width for first order formulae","authors":"Isolde Adler, M. Weyer","doi":"10.2168/LMCS-8(1:32)2012","DOIUrl":"https://doi.org/10.2168/LMCS-8(1:32)2012","url":null,"abstract":"We introduce tree-width for first order formulae phi, fotw(phi). We show\u0000that computing fotw is fixed-parameter tractable with parameter fotw. Moreover,\u0000we show that on classes of formulae of bounded fotw, model checking is fixed\u0000parameter tractable, with parameter the length of the formula. This is done by\u0000translating a formula phi with fotw(phi)<k into a formula of the k-variable\u0000fragment L^k of first order logic. For fixed k, the question whether a given\u0000first order formula is equivalent to an L^k formula is undecidable. In\u0000contrast, the classes of first order formulae with bounded fotw are fragments\u0000of first order logic for which the equivalence is decidable.\u0000 Our notion of tree-width generalises tree-width of conjunctive queries to\u0000arbitrary formulae of first order logic by taking into account the quantifier\u0000interaction in a formula. Moreover, it is more powerful than the notion of\u0000elimination-width of quantified constraint formulae, defined by Chen and Dalmau\u0000(CSL 2005): for quantified constraint formulae, both bounded elimination-width\u0000and bounded fotw allow for model checking in polynomial time. We prove that\u0000fotw of a quantified constraint formula phi is bounded by the\u0000elimination-width of phi, and we exhibit a class of quantified constraint\u0000formulae with bounded fotw, that has unbounded elimination-width. A similar\u0000comparison holds for strict tree-width of non-recursive stratified datalog as\u0000defined by Flum, Frick, and Grohe (JACM 49, 2002).\u0000 Finally, we show that fotw has a characterization in terms of a cops and\u0000robbers game without monotonicity cost.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2012-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67823829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-07-05DOI: 10.2168/LMCS-10(1:7)2014
Stefan Goller, Markus Lohrey
We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.
{"title":"The Complexity of the First-Order Theory of Ground Tree Rewrite Graphs","authors":"Stefan Goller, Markus Lohrey","doi":"10.2168/LMCS-10(1:7)2014","DOIUrl":"https://doi.org/10.2168/LMCS-10(1:7)2014","url":null,"abstract":"We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2011-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73083441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-04-18DOI: 10.2168/LMCS-10(1:13)2014
Tom'avs Br'azdil, V'aclav Brovzek, K. Chatterjee, Vojtvech Forejt, Anton'in Kuvcera
We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k limit-average functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the case of one limit-average function, both randomization and memory are necessary for strategies even for epsilon-approximation, and that finite-memory randomized strategies are sufficient for achieving Pareto optimal values. Under the satisfaction objective, in contrast to the case of one limit-average function, infinite memory is necessary for strategies achieving a specific value (i.e. randomized finite-memory strategies are not sufficient), whereas memoryless randomized strategies are sufficient for epsilon-approximation, for all epsilon>0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of limit-average functions, for all epsilon>0. Our analysis also reveals flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, corrects the flaws, and allows us to obtain improved results.
{"title":"Markov Decision Processes with Multiple Long-Run AverageObjectives","authors":"Tom'avs Br'azdil, V'aclav Brovzek, K. Chatterjee, Vojtvech Forejt, Anton'in Kuvcera","doi":"10.2168/LMCS-10(1:13)2014","DOIUrl":"https://doi.org/10.2168/LMCS-10(1:13)2014","url":null,"abstract":"We study Markov decision processes (MDPs) with multiple\u0000limit-average (or mean-payoff) functions. We consider two\u0000different objectives, namely, expectation and satisfaction\u0000objectives. Given an MDP with k limit-average functions, in the\u0000expectation objective the goal is to maximize the expected\u0000limit-average value, and in the satisfaction objective the goal\u0000is to maximize the probability of runs such that the\u0000limit-average value stays above a given vector. We show that\u0000under the expectation objective, in contrast to the case of one\u0000limit-average function, both randomization and memory are\u0000necessary for strategies even for epsilon-approximation, and\u0000that finite-memory randomized strategies are sufficient for\u0000achieving Pareto optimal values. Under the satisfaction\u0000objective, in contrast to the case of one limit-average\u0000function, infinite memory is necessary for strategies achieving\u0000a specific value (i.e. randomized finite-memory strategies are\u0000not sufficient), whereas memoryless randomized strategies are\u0000sufficient for epsilon-approximation, for all epsilon>0. We\u0000further prove that the decision problems for both expectation\u0000and satisfaction objectives can be solved in polynomial time\u0000and the trade-off curve (Pareto curve) can be\u0000epsilon-approximated in time polynomial in the size of the MDP\u0000and 1/epsilon, and exponential in the number of limit-average\u0000functions, for all epsilon>0. Our analysis also reveals flaws\u0000in previous work for MDPs with multiple mean-payoff functions\u0000under the expectation objective, corrects the flaws, and allows\u0000us to obtain improved results.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2011-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67822621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-12-06DOI: 10.2168/LMCS-8(3:30)2012
Predrag Janičić
There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system for uniform solving of a wide class of problems by reducing them to SAT. The system uses a new specification language URSA that combines imperative and declarative programming paradigms. The reduction to SAT is defined precisely by the semantics of the specification language. The domain of the approach is wide (e.g., many NP-complete problems can be simply specified and then solved by the system) and there are problems easily solvable by the proposed system, while they can be hardly solved by using other programming languages or constraint programming systems. So, the system can be seen not only as a tool for solving problems by reducing them to SAT, but also as a general-purpose constraint solving system (for finite domains). In this paper, we also describe an open-source implementation of the described approach. The performed experiments suggest that the system is competitive to state-of-the-art related modelling systems.
{"title":"URSA: A System for Uniform Reduction to SAT","authors":"Predrag Janičić","doi":"10.2168/LMCS-8(3:30)2012","DOIUrl":"https://doi.org/10.2168/LMCS-8(3:30)2012","url":null,"abstract":"There are a huge number of problems, from various areas, being solved by\u0000reducing them to SAT. However, for many applications, translation into SAT is\u0000performed by specialized, problem-specific tools. In this paper we describe a\u0000new system for uniform solving of a wide class of problems by reducing them to\u0000SAT. The system uses a new specification language URSA that combines imperative\u0000and declarative programming paradigms. The reduction to SAT is defined\u0000precisely by the semantics of the specification language. The domain of the\u0000approach is wide (e.g., many NP-complete problems can be simply specified and\u0000then solved by the system) and there are problems easily solvable by the\u0000proposed system, while they can be hardly solved by using other programming\u0000languages or constraint programming systems. So, the system can be seen not\u0000only as a tool for solving problems by reducing them to SAT, but also as a\u0000general-purpose constraint solving system (for finite domains). In this paper,\u0000we also describe an open-source implementation of the described approach. The\u0000performed experiments suggest that the system is competitive to\u0000state-of-the-art related modelling systems.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2010-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67823972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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