Theory of Computing Systems最新文献

{"title":"Visit-Bounded Stack Automata","authors":"Jozef Jirásek, Ian McQuillan","doi":"10.1007/s00224-023-10124-0","DOIUrl":"https://doi.org/10.1007/s00224-023-10124-0","url":null,"abstract":"<p>An automaton is <i>k-visit-bounded</i> if during any computation its work tape head visits each tape cell at most <i>k</i> times. In this paper we consider stack automata which are <i>k</i>-visit-bounded for some integer <i>k</i>. This restriction resets the visits when popping (unlike similarly defined Turing machine restrictions) which we show allows the model to accept a proper superset of context-free languages and also a proper superset of languages of visit-bounded Turing machines. We study two variants of visit-bounded stack automata: one where only instructions that move the stack head downwards increase the number of visits of the destination cell, and another where any transition increases the number of visits. We prove that the two types of automata recognize the same languages. We then show that all languages recognized by visit-bounded stack automata are effectively semilinear, and hence are letter-equivalent to regular languages, which can be used to show other properties.</p>","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unit Read-once Refutations for Systems of Difference Constraints","authors":"K. Subramani, P. Wojciechowski","doi":"10.1007/s00224-023-10134-y","DOIUrl":"https://doi.org/10.1007/s00224-023-10134-y","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41737660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Foreword: a Commemorative Issue for Alan L. Selman","authors":"E. Mayordomo, M. Ogihara, A. Rudra","doi":"10.1007/s00224-023-10123-1","DOIUrl":"https://doi.org/10.1007/s00224-023-10123-1","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42059463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computing a Partition Function of a Generalized Pattern-Based Energy over a Semiring","authors":"Rustem Takhanov","doi":"10.1007/s00224-023-10128-w","DOIUrl":"https://doi.org/10.1007/s00224-023-10128-w","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41667781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subgroup Membership in GL(2,Z)","authors":"Markus Lohrey","doi":"10.4230/LIPIcs.STACS.2021.51","DOIUrl":"https://doi.org/10.4230/LIPIcs.STACS.2021.51","url":null,"abstract":"It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time when all group elements are represented by so-called power words, i.e., words of the form $$p_1^{z_1} p_2^{z_2} cdots p_k^{z_k}$$ p 1 z 1 p 2 z 2 ⋯ p k z k . Here the $$p_i$$ p i are explicit words over the generating set of the group and all $$z_i$$ z i are binary encoded integers. As a corollary, it follows that the subgroup membership problem for the matrix group $$textsf{GL}(2,mathbb {Z})$$ GL ( 2 , Z ) can be decided in polynomial time when elements of $$textsf{GL}(2,mathbb {Z})$$ GL ( 2 , Z ) are represented by matrices with binary encoded integers. For the same input representation, it also shown that one can compute in polynomial time the index of a given finitely generated subgroup of $$textsf{GL}(2,mathbb {Z})$$ GL ( 2 , Z ) .","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46738350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subgroup Membership in GL(2,Z)","authors":"Markus Lohrey","doi":"10.1007/s00224-023-10122-2","DOIUrl":"https://doi.org/10.1007/s00224-023-10122-2","url":null,"abstract":"Abstract It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time when all group elements are represented by so-called power words, i.e., words of the form $$p_1^{z_1} p_2^{z_2} cdots p_k^{z_k}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mn>1</mml:mn> <mml:msub> <mml:mi>z</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:msubsup> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:msubsup> <mml:mo>⋯</mml:mo> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mi>k</mml:mi> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:msubsup> </mml:mrow> </mml:math> . Here the $$p_i$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> are explicit words over the generating set of the group and all $$z_i$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> are binary encoded integers. As a corollary, it follows that the subgroup membership problem for the matrix group $$textsf{GL}(2,mathbb {Z})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>GL</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>Z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> can be decided in polynomial time when elements of $$textsf{GL}(2,mathbb {Z})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>GL</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>Z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> are represented by matrices with binary encoded integers. For the same input representation, it also shown that one can compute in polynomial time the index of a given finitely generated subgroup of $$textsf{GL}(2,mathbb {Z})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>GL</mml:mi> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>Z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135806947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reachability in Two-Parametric Timed Automata with one Parameter is EXPSPACE-Complete","authors":"Stefan Göller, Mathieu Hilaire","doi":"10.1007/s00224-023-10121-3","DOIUrl":"https://doi.org/10.1007/s00224-023-10121-3","url":null,"abstract":"Abstract Parametric timed automata (PTA) have been introduced by Alur, Henzinger, and Vardi as an extension of timed automata in which clocks can be compared against parameters. The reachability problem asks for the existence of an assignment of the parameters to the non-negative integers such that reachability holds in the underlying timed automaton. The reachability problem for PTA is long known to be undecidable, already over three parametric clocks. A few years ago, Bundala and Ouaknine proved that for PTA over two parametric clocks and one parameter the reachability problem is decidable and also showed a lower bound for the complexity class P S P A C E N E X P . Our main result is that the reachability problem for two-parametric timed automata with one parameter is E X P S P A C E -complete. Our contribution is two-fold. For the E X P S P A C E lower bound, inspired by [13, 14], we make use of deep results from complexity theory, namely a serializability characterization of E X P S P A C E (in turn based on Barrington’s Theorem) and a logspace translation of numbers in Chinese remainder representation to binary representation due to Chiu, Davida, and Litow. It is shown that with small PTA over two parametric clocks and one parameter one can simulate serializability computations. For the E X P S P A C E upper bound, we first give a careful exponential time reduction from PTA over two parametric clocks and one parameter to a (slight subclass of) parametric one-counter automata over one parameter based on a minor adjustment of a construction due to Bundala and Ouaknine. For solving the reachability problem for parametric one-counter automata with one parameter, we provide a series of techniques to partition a fictitious run into several carefully chosen subruns that allow us to prove that it is sufficient to consider a parameter value of exponential magnitude only. This allows us to show a doubly-exponential upper bound on the value of the only parameter of a PTA over two parametric clocks and one parameter. We hope that extensions of our techniques lead to finally establishing decidability of the long-standing open problem of reachability in parametric timed automata with two parametric clocks (and arbitrarily many parameters) and, if decidability holds, determinining its precise computational complexity.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135223285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to: On the Transformation of LL(k)-linear to LL(1)-linear Grammars","authors":"I. Olkhovsky, A. Okhotin","doi":"10.1007/s00224-023-10120-4","DOIUrl":"https://doi.org/10.1007/s00224-023-10120-4","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47920146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Hierarchy of Swarm-automaton for the Number of Agents","authors":"Kaoru Fujioka","doi":"10.1007/s00224-023-10117-z","DOIUrl":"https://doi.org/10.1007/s00224-023-10117-z","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47310883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial-Time Axioms of Choice and Polynomial-Time Cardinality","authors":"Joshua A. Grochow","doi":"10.1007/s00224-023-10118-y","DOIUrl":"https://doi.org/10.1007/s00224-023-10118-y","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44649146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}