Mathematical Structures in Computer Science最新文献

{"title":"Equational theorem proving for clauses over strings","authors":"Dohan Kim","doi":"10.1017/s0960129524000112","DOIUrl":"https://doi.org/10.1017/s0960129524000112","url":null,"abstract":"<p>Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus with strings and present an equational theorem proving framework for clauses over strings. It provides a saturation procedure for clauses over strings and show that the proposed superposition calculus with contraction rules is refutationally complete. In particular, this paper presents a new decision procedure for solving word problems over strings and provides a new method of solving unification problems over strings w.r.t. a set of conditional equations <span>R</span> over strings if <span>R</span> can be finitely saturated under the proposed inference system with contraction rules.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609589","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":"An approximation algorithm for the -prize-collecting multicut problem in trees with submodular penalties","authors":"Xiaofei Liu, Weidong Li","doi":"10.1017/s0960129524000124","DOIUrl":"https://doi.org/10.1017/s0960129524000124","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000124_inline3.png\" /> <jats:tex-math> $T=(V,E)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a tree in which each edge is assigned a cost; let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000124_inline4.png\" /> <jats:tex-math> $mathcal{P}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a set of source–sink pairs of vertices in <jats:italic>V</jats:italic> in which each source–sink pair produces a profit. Given a lower bound <jats:italic>K</jats:italic> for the profit, the <jats:italic>K</jats:italic>-prize-collecting multicut problem in trees with submodular penalties is to determine a partial multicut <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000124_inline5.png\" /> <jats:tex-math> $Msubseteq E$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> such that the total profit of the disconnected pairs after removing <jats:italic>M</jats:italic> from <jats:italic>T</jats:italic> is at least <jats:italic>K</jats:italic>, and the total cost of edges in <jats:italic>M</jats:italic> plus the penalty of the set of still-connected pairs is minimized, where the penalty is determined by a nondecreasing submodular function. Based on the primal-dual scheme, we present a combinatorial polynomial-time algorithm by carefully increasing the penalty. In the theoretical analysis, we prove that the approximation factor of the proposed algorithm is <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000124_inline6.png\" /> <jats:tex-math> $(frac{8}{3}+frac{4}{3}kappa+varepsilon)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000124_inline7.png\" /> <jats:tex-math> $kappa$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is the total curvature of the submodular function and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000124_inline8.png\" /> <jats:tex-math> $varepsilon$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is any fixed positive number. Experiments reveal that the objective value of the solutions generated by the proposed algorithm is less than 130% compared with that of the optimal value in most cases.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"3 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609460","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":"A 2-categorical proof of Frobenius for fibrations defined from a generic point","authors":"Sina Hazratpour, Emily Riehl","doi":"10.1017/s0960129524000094","DOIUrl":"https://doi.org/10.1017/s0960129524000094","url":null,"abstract":"Consider a locally cartesian closed category with an object <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000094_inline1.png\" /> <jats:tex-math> $mathbb{I}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential with the generic point of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000094_inline2.png\" /> <jats:tex-math> $mathbb{I}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> defines a trivial fibration. Then the fibrations are also closed under pushforward.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"33 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563818","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":"A set-theoretic approach to algebraic L-domains","authors":"Juan Zou, Yuhan Zhao, Cuixia Miao, Longchun Wang","doi":"10.1017/s0960129524000069","DOIUrl":"https://doi.org/10.1017/s0960129524000069","url":null,"abstract":"In this paper, the notion of locally algebraic intersection structure is introduced for algebraic L-domains. Essentially, every locally algebraic intersection structure is a family of sets, which forms an algebraic L-domain ordered by inclusion. It is shown that there is a locally algebraic intersection structure which is order-isomorphic to a given algebraic L-domain. This result extends the classic Stone’s representation theorem for Boolean algebras to the case of algebraic L-domains. In addition, it can be seen that many well-known representations of algebraic L-domains, such as logical algebras, information systems, closure spaces, and formal concept analysis, can be analyzed in the framework of locally algebraic intersection structures. Then, a set-theoretic uniformity across different representations of algebraic L-domains is established.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"43 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140563806","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":"Dimension in team semantics","authors":"Lauri Hella, Kerkko Luosto, Jouko Väänänen","doi":"10.1017/s0960129524000021","DOIUrl":"https://doi.org/10.1017/s0960129524000021","url":null,"abstract":"<p>We introduce three measures of complexity for families of sets. Each of the three measures, which we call dimensions, is defined in terms of the minimal number of convex subfamilies that are needed for covering the given family. For upper dimension, the subfamilies are required to contain a unique maximal set, for dual upper dimension a unique minimal set, and for cylindrical dimension both a unique maximal and a unique minimal set. In addition to considering dimensions of particular families of sets, we study the behavior of dimensions under operators that map families of sets to new families of sets. We identify natural sufficient criteria for such operators to preserve the growth class of the dimensions. We apply the theory of our dimensions for proving new hierarchy results for logics with team semantics. To this end we associate each atom with a natural notion or arity. First, we show that the standard logical operators preserve the growth classes of the families arising from the semantics of formulas in such logics. Second, we show that the upper dimension of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311153531332-0533:S0960129524000021:S0960129524000021_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$k+1$</span></span></img></span></span>-ary dependence, inclusion, independence, anonymity, and exclusion atoms is in a strictly higher growth class than that of any <span>k</span>-ary atoms, whence the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311153531332-0533:S0960129524000021:S0960129524000021_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$k+1$</span></span></img></span></span>-ary atoms are not definable in terms of any atoms of smaller arity.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"43 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140107620","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":"Implicational Kleene algebra with domain and the substructural logic of partial correctness","authors":"Igor Sedlár","doi":"10.1017/s0960129524000045","DOIUrl":"https://doi.org/10.1017/s0960129524000045","url":null,"abstract":"<p>We show that Kozen and Tiuryn’s substructural logic of partial correctness <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240301160033202-0894:S0960129524000045:S0960129524000045_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf{S}$</span></span></img></span></span> embeds into the equational theory of Kleene algebra with domain, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240301160033202-0894:S0960129524000045:S0960129524000045_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf{KAD}$</span></span></img></span></span>. We provide an implicational formulation of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240301160033202-0894:S0960129524000045:S0960129524000045_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf{KAD}$</span></span></img></span></span> which sets <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240301160033202-0894:S0960129524000045:S0960129524000045_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathsf{S}$</span></span></img></span></span> in the context of implicational extensions of Kleene algebra.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025695","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":"Parameterized complexity of weighted team definability","authors":"Juha Kontinen, Yasir Mahmood, Arne Meier, Heribert Vollmer","doi":"10.1017/s0960129524000033","DOIUrl":"https://doi.org/10.1017/s0960129524000033","url":null,"abstract":"In this article, we study the complexity of weighted team definability for logics with team semantics. This problem is a natural analog of one of the most studied problems in parameterized complexity, the notion of weighted Fagin-definability, which is formulated in terms of satisfaction of first-order formulas with free relation variables. We focus on the parameterized complexity of weighted team definability for a fixed formula <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000033_inline1.png\" /> <jats:tex-math> $varphi$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of central team-based logics. Given a first-order structure <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000033_inline2.png\" /> <jats:tex-math> $mathcal{A}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and the parameter value <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000033_inline3.png\" /> <jats:tex-math> $kin mathbb N$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> as input, the question is to determine whether <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000033_inline4.png\" /> <jats:tex-math> $mathcal{A},Tmodels varphi$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for some team <jats:italic>T</jats:italic> of size <jats:italic>k</jats:italic>. We show several results on the complexity of this problem for dependence, independence, and inclusion logic formulas. Moreover, we also relate the complexity of weighted team definability to the complexity classes in the well-known W-hierarchy as well as paraNP.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"36 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139924735","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":"Discrete equational theories","authors":"J. Rosický","doi":"10.1017/s096012952400001x","DOIUrl":"https://doi.org/10.1017/s096012952400001x","url":null,"abstract":"<p>On a locally <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240119162700723-0670:S096012952400001X:S096012952400001X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span>-presentable symmetric monoidal closed category <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240119162700723-0670:S096012952400001X:S096012952400001X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {V}$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240119162700723-0670:S096012952400001X:S096012952400001X_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span>-ary enriched equational theories correspond to enriched monads preserving <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240119162700723-0670:S096012952400001X:S096012952400001X_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span>-filtered colimits. We introduce discrete <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240119162700723-0670:S096012952400001X:S096012952400001X_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span>-ary enriched equational theories where operations are induced by those having discrete arities (equations are not required to have discrete arities) and show that they correspond to enriched monads preserving preserving <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240119162700723-0670:S096012952400001X:S096012952400001X_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span>-filtered colimits and surjections. Using it, we prove enriched Birkhof-type theorems for categories of algebras of discrete theories. This extends known results from metric spaces and posets to general symmetric monoidal closed categories.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"3 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139516927","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":"A construction of free dcpo-cones","authors":"Yuxu Chen, Hui Kou, Zhenchao Lyu, Xiaolin Xie","doi":"10.1017/s0960129523000427","DOIUrl":"https://doi.org/10.1017/s0960129523000427","url":null,"abstract":"<p>We give a construction of the free dcpo-cone over any dcpo. There are two steps for getting this result. Firstly, we extend the notion of power domain to directed spaces which are equivalent to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240109154214644-0603:S0960129523000427:S0960129523000427_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$T_0$</span></span></img></span></span> monotone-determined spaces introduced by Erné, and we construct the probabilistic powerspace of the monotone determined space, which is defined as a free monotone determined cone. Secondly, we take D-completion of the free monotone determined cone over the dcpo with its Scott topology. In addition, we show that generally the valuation power domain of any dcpo is not the free dcpo-cone.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139413455","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":"Game characterizations for the number of quantifiers","authors":"Lauri Hella, Kerkko Luosto","doi":"10.1017/s0960129523000415","DOIUrl":"https://doi.org/10.1017/s0960129523000415","url":null,"abstract":"<p>A game that characterizes equivalence of structures with respect to all first-order sentences containing a given number of quantifiers was introduced by Immerman in 1981. We define three other games and prove that they are all equivalent to the Immerman game, and hence also give a characterization for the number of quantifiers needed for separating structures. In the Immerman game, Duplicator has a canonical optimal strategy, and hence Duplicator can be completely removed from the game by replacing her moves with default moves given by this optimal strategy. On the other hand, in the last two of our games there is no such optimal strategy for Duplicator. Thus, the Immerman game can be regarded as a one-player game, but two of our games are genuine two-player games.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"21 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139413500","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}