Pub Date : 2010-08-04DOI: 10.2168/LMCS-9(3:27)2013
Cameron E. Freer, Bjoern Kjos-Hanssen
We obtain a non-implication result in the Medvedev degrees by studying sequences that are close to Martin-L"of random in asymptotic Hamming distance. Our result is that the class of stochastically bi-immune sets is not Medvedev reducible to the class of sets having complex packing dimension 1.
{"title":"Randomness extraction and asymptotic Hamming distance","authors":"Cameron E. Freer, Bjoern Kjos-Hanssen","doi":"10.2168/LMCS-9(3:27)2013","DOIUrl":"https://doi.org/10.2168/LMCS-9(3:27)2013","url":null,"abstract":"We obtain a non-implication result in the Medvedev degrees by studying\u0000sequences that are close to Martin-L\"of random in asymptotic Hamming distance.\u0000Our result is that the class of stochastically bi-immune sets is not Medvedev\u0000reducible to the class of sets having complex packing dimension 1.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2010-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824988","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 : 2009-05-25DOI: 10.2168/LMCS-7(3:15)2011
P. Hyvernat
This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence possible and conceptually interesting is the use of the infinite Ramsey theorem. Along the way, the question of the cardinality of the collection of finiteness spaces on N is answered. Basic knowledge about coherent spaces and finiteness spaces is assumed.
{"title":"Coherent and finiteness spaces","authors":"P. Hyvernat","doi":"10.2168/LMCS-7(3:15)2011","DOIUrl":"https://doi.org/10.2168/LMCS-7(3:15)2011","url":null,"abstract":"This short note presents a new relation between coherent spaces and\u0000finiteness spaces. This takes the form of a functor from COH to FIN commuting\u0000with the additive and multiplicative structure of linear logic. What makes this\u0000correspondence possible and conceptually interesting is the use of the infinite\u0000Ramsey theorem. Along the way, the question of the cardinality of the\u0000collection of finiteness spaces on N is answered. Basic knowledge about\u0000coherent spaces and finiteness spaces is assumed.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2009-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824206","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 : 2009-03-22DOI: 10.2168/LMCS-8(1:11)2012
P. Arrighi, Alejandro Díaz-Caro
The algebraic �-calculus (40) and the linear-algebraic �-calculus (3) extend the �-calculus with the possibility of making arbitrary linear combinations of �-calculus terms (preserving Pi:ti). In this paper we provide a fine-grained, System F -like type system for the linear-algebraic �-calculus (Lineal). We show that this scalar type system enjoys both the subject-reduction property and the strong-normalisation property, which constitute our main technical results. The latter yields a significant simplification of the linear-algebraic �-calculus itself, by removing the need for some restrictions in its reduction rules - and thus leaving it more intuitive. But the more important, original feature of this scalar type system is that it keeps track of 'the amount of a type' that this present in each term. As an example, we show how to use this type system in order to guarantee the well-definiteness of probabilistic functions ( Pi = 1) - thereby specializing Lineal into a probabilistic, higher-order �-calculus. Finally we begin to investigate the logic induced by the scalar type system, and prove a no-cloning theorem expressed solely in terms of the possible proof methods in this logic. We discuss the potential connections with Linear Logic and Quantum Computation.
{"title":"A System F accounting for scalars","authors":"P. Arrighi, Alejandro Díaz-Caro","doi":"10.2168/LMCS-8(1:11)2012","DOIUrl":"https://doi.org/10.2168/LMCS-8(1:11)2012","url":null,"abstract":"The algebraic �-calculus (40) and the linear-algebraic �-calculus (3) extend the �-calculus with the possibility of making arbitrary linear combinations of �-calculus terms (preserving Pi:ti). In this paper we provide a fine-grained, System F -like type system for the linear-algebraic �-calculus (Lineal). We show that this scalar type system enjoys both the subject-reduction property and the strong-normalisation property, which constitute our main technical results. The latter yields a significant simplification of the linear-algebraic �-calculus itself, by removing the need for some restrictions in its reduction rules - and thus leaving it more intuitive. But the more important, original feature of this scalar type system is that it keeps track of 'the amount of a type' that this present in each term. As an example, we show how to use this type system in order to guarantee the well-definiteness of probabilistic functions ( Pi = 1) - thereby specializing Lineal into a probabilistic, higher-order �-calculus. Finally we begin to investigate the logic induced by the scalar type system, and prove a no-cloning theorem expressed solely in terms of the possible proof methods in this logic. We discuss the potential connections with Linear Logic and Quantum Computation.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"8 1","pages":"11"},"PeriodicalIF":0.6,"publicationDate":"2009-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67823740","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}
Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The "permutation-enumeration" algorithm performs an exhaustive search among these strategies, while the "permutation-improvement'' algorithm is based on successive improvements, a la Hoffman-Karp. Our algorithms improve previously known algorithms in several aspects. First they run in polynomial time when the number of random vertices is fixed, so the problem of solving simple stochastic games is fixed-parameter tractable when the parameter is the number of random vertices. Furthermore, our algorithms do not require the input game to be transformed into a stopping game. Finally, the permutation-enumeration algorithm does not use linear programming, while the permutation-improvement algorithm may run in polynomial time.
{"title":"Solving Simple Stochastic Games with Few Random Vertices","authors":"H. Gimbert, Florian Horn","doi":"10.2168/LMCS-5(2:9)2009","DOIUrl":"https://doi.org/10.2168/LMCS-5(2:9)2009","url":null,"abstract":"Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The \"permutation-enumeration\" algorithm performs an exhaustive search among these strategies, while the \"permutation-improvement'' algorithm is based on successive improvements, a la Hoffman-Karp. Our algorithms improve previously known algorithms in several aspects. First they run in polynomial time when the number of random vertices is fixed, so the problem of solving simple stochastic games is fixed-parameter tractable when the parameter is the number of random vertices. Furthermore, our algorithms do not require the input game to be transformed into a stopping game. Finally, the permutation-enumeration algorithm does not use linear programming, while the permutation-improvement algorithm may run in polynomial time.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"43 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2007-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80214591","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 : 2007-01-05DOI: 10.2168/LMCS-5(2:14)2009
Guillaume Bonfante, Yves Guiraud
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a Turing-complete computational model. Their algebraic structure is used by analysis tools, called polygraphic interpretations, for complexity analysis. In particular, we delineate a subclass of polygraphic programs that compute exactly the functions that are Turing-computable in polynomial time.
{"title":"Polygraphic programs and polynomial-time functions","authors":"Guillaume Bonfante, Yves Guiraud","doi":"10.2168/LMCS-5(2:14)2009","DOIUrl":"https://doi.org/10.2168/LMCS-5(2:14)2009","url":null,"abstract":"We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a Turing-complete computational model. Their algebraic structure is used by analysis tools, called polygraphic interpretations, for complexity analysis. In particular, we delineate a subclass of polygraphic programs that compute exactly the functions that are Turing-computable in polynomial time.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"5 1","pages":"1-37"},"PeriodicalIF":0.6,"publicationDate":"2007-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824101","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}
{"title":"Modularizing the Elimination of r=0 in Kleene Algebra","authors":"Nobody Anonymous","doi":"10.2168/LMCS-1(3:5)2005","DOIUrl":"https://doi.org/10.2168/LMCS-1(3:5)2005","url":null,"abstract":"","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67822537","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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