{"title":"Distributed Asynchronous Games With Causal Memory are Undecidable","authors":"H. Gimbert","doi":"10.46298/lmcs-18(3:30)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:30)2022","url":null,"abstract":"We show the undecidability of the distributed control problem when the plant\u0000is an asynchronous automaton, the controllers use causal memory and the goal of\u0000the controllers is to put each process in a local accepting state.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130371697","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":"A Functional Abstraction of Typed Invocation Contexts","authors":"Youyou Cong, Chiaki Ishio, Kaho Honda, K. Asai","doi":"10.46298/lmcs-18(3:34)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:34)2022","url":null,"abstract":"In their paper \"A Functional Abstraction of Typed Contexts\", Danvy and\u0000Filinski show how to derive a monomorphic type system of the shift and reset\u0000operators from a CPS semantics. In this paper, we show how this method scales\u0000to Felleisen's control and prompt operators. Compared to shift and reset,\u0000control and prompt exhibit a more dynamic behavior, in that they can manipulate\u0000a trail of contexts surrounding the invocation of previously captured\u0000continuations. Our key observation is that, by adopting a functional\u0000representation of trails in the CPS semantics, we can derive a type system that\u0000encodes all and only constraints imposed by the CPS semantics.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133944225","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":"Deciding All Behavioral Equivalences at Once: A Game for Linear-time-Branching-time Spectroscopy","authors":"Benjamin Bisping, U. Nestmann","doi":"10.46298/lmcs-18(3:19)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:19)2022","url":null,"abstract":"We introduce a generalization of the bisimulation game that finds\u0000distinguishing Hennessy-Milner logic formulas from every finitary,\u0000subformula-closed language in van Glabbeek's linear-time--branching-time\u0000spectrum between two finite-state processes. We identify the relevant\u0000dimensions that measure expressive power to yield formulas belonging to the\u0000coarsest distinguishing behavioral preorders and equivalences; the compared\u0000processes are equivalent in each coarser behavioral equivalence from the\u0000spectrum. We prove that the induced algorithm can determine the best fit of\u0000(in)equivalences for a pair of processes.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116693446","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":"Small Promise CSPs that reduce to large CSPs","authors":"Alexandr Kazda, P. Mayr, Dmitriy Zhuk","doi":"10.46298/lmcs-18(3:25)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:25)2022","url":null,"abstract":"For relational structures A, B of the same signature, the Promise Constraint\u0000Satisfaction Problem PCSP(A,B) asks whether a given input structure maps\u0000homomorphically to A or does not even map to B. We are promised that the input\u0000satisfies exactly one of these two cases.\u0000 If there exists a structure C with homomorphisms $Ato Cto B$, then\u0000PCSP(A,B) reduces naturally to CSP(C). To the best of our knowledge all known\u0000tractable PCSPs reduce to tractable CSPs in this way. However Barto showed that\u0000some PCSPs over finite structures A, B require solving CSPs over infinite C.\u0000 We show that even when such a reduction to finite C is possible, this\u0000structure may become arbitrarily large. For every integer $n>1$ and every prime\u0000p we give A, B of size n with a single relation of arity $n^p$ such that\u0000PCSP(A, B) reduces via a chain of homomorphisms $ Ato Cto B$ to a tractable\u0000CSP over some C of size p but not over any smaller structure. In a second\u0000family of examples, for every prime $pgeq 7$ we construct A, B of size $p-1$\u0000with a single ternary relation such that PCSP(A, B) reduces via $Ato Cto B$\u0000to a tractable CSP over some C of size p but not over any smaller structure. In\u0000contrast we show that if A, B are graphs and PCSP(A,B) reduces to tractable\u0000CSP(C) for some finite digraph C, then already A or B has a tractable CSP. This\u0000extends results and answers a question of Deng et al.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"275 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132624623","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":"Coalgebras for Bisimulation of Weighted Automata over Semirings","authors":"Purandar Bhaduri","doi":"10.46298/lmcs-19(1:4)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(1:4)2023","url":null,"abstract":"Weighted automata are a generalization of nondeterministic automata that\u0000associate a weight drawn from a semiring $K$ with every transition and every\u0000state. Their behaviours can be formalized either as weighted language\u0000equivalence or weighted bisimulation. In this paper we explore the properties\u0000of weighted automata in the framework of coalgebras over (i) the category\u0000$mathsf{SMod}$ of semimodules over a semiring $K$ and $K$-linear maps, and\u0000(ii) the category $mathsf{Set}$ of sets and maps. We show that the behavioural\u0000equivalences defined by the corresponding final coalgebras in these two cases\u0000characterize weighted language equivalence and weighted bisimulation,\u0000respectively. These results extend earlier work by Bonchi et al. using the\u0000category $mathsf{Vect}$ of vector spaces and linear maps as the underlying\u0000model for weighted automata with weights drawn from a field $K$. The key step\u0000in our work is generalizing the notions of linear relation and linear\u0000bisimulation of Boreale from vector spaces to semimodules using the concept of\u0000the kernel of a $K$-linear map in the sense of universal algebra. We also\u0000provide an abstract procedure for forward partition refinement for computing\u0000weighted language equivalence. Since for weighted automata defined over\u0000semirings the problem is undecidable in general, it is guaranteed to halt only\u0000in special cases. We provide sufficient conditions for the termination of our\u0000procedure. Although the results are similar to those of Bonchi et al., many of\u0000our proofs are new, especially those about the coalgebra in $mathsf{SMod}$\u0000characterizing weighted language equivalence.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"308 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113985248","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":"Convexity via Weak Distributive Laws","authors":"F. Bonchi, A. Santamaria","doi":"10.46298/lmcs-18(4:8)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(4:8)2022","url":null,"abstract":"We study the canonical weak distributive law $delta$ of the powerset monad\u0000over the semimodule monad for a certain class of semirings containing, in\u0000particular, positive semifields. For this subclass we characterise $delta$ as\u0000a convex closure in the free semimodule of a set. Using the abstract theory of\u0000weak distributive laws, we compose the powerset and the semimodule monads via\u0000$delta$, obtaining the monad of convex subsets of the free semimodule.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114632538","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":"Linear equations for unordered data vectors in $[D]^kto{}Z^d$","authors":"Piotr Hofman, Jakub R'o.zycki","doi":"10.46298/lmcs-18(4:11)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(4:11)2022","url":null,"abstract":"Following a recently considered generalisation of linear equations to\u0000unordered-data vectors and to ordered-data vectors, we perform a further\u0000generalisation to data vectors that are functions from k-element subsets of the\u0000unordered-data set to vectors of integer numbers. These generalised equations\u0000naturally appear in the analysis of vector addition systems (or Petri nets)\u0000extended so that each token carries a set of unordered data. We show that\u0000nonnegative-integer solvability of linear equations is in nondeterministic\u0000exponential time while integer solvability is in polynomial time.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131132277","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":"Addressing Machines as models of lambda-calculus","authors":"G. D. Penna, B. Intrigila, Giulio Manzonetto","doi":"10.46298/lmcs-18(3:10)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:10)2022","url":null,"abstract":"Turing machines and register machines have been used for decades in\u0000theoretical computer science as abstract models of computation. Also the\u0000$lambda$-calculus has played a central role in this domain as it allows to\u0000focus on the notion of functional computation, based on the substitution\u0000mechanism, while abstracting away from implementation details. The present\u0000article starts from the observation that the equivalence between these\u0000formalisms is based on the Church-Turing Thesis rather than an actual encoding\u0000of $lambda$-terms into Turing (or register) machines. The reason is that these\u0000machines are not well-suited for modelling $lambda$-calculus programs.\u0000 We study a class of abstract machines that we call \"addressing machine\" since\u0000they are only able to manipulate memory addresses of other machines. The\u0000operations performed by these machines are very elementary: load an address in\u0000a register, apply a machine to another one via their addresses, and call the\u0000address of another machine. We endow addressing machines with an operational\u0000semantics based on leftmost reduction and study their behaviour. The set of\u0000addresses of these machines can be easily turned into a combinatory algebra. In\u0000order to obtain a model of the full untyped $lambda$-calculus, we need to\u0000introduce a rule that bares similarities with the $omega$-rule and the rule\u0000$zeta_beta$ from combinatory logic.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115754126","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":"LNL polycategories and doctrines of linear logic","authors":"Michael Shulman","doi":"10.46298/lmcs-19(2:1)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(2:1)2023","url":null,"abstract":"We define and study LNL polycategories, which abstract the judgmental\u0000structure of classical linear logic with exponentials. Many existing structures\u0000can be represented as LNL polycategories, including LNL adjunctions, linear\u0000exponential comonads, LNL multicategories, IL-indexed categories, linearly\u0000distributive categories with storage, commutative and strong monads,\u0000CBPV-structures, models of polarized calculi, Freyd-categories, and skew\u0000multicategories, as well as ordinary cartesian, symmetric, and planar\u0000multicategories and monoidal categories, symmetric polycategories, and linearly\u0000distributive and *-autonomous categories. To study such classes of structures\u0000uniformly, we define a notion of LNL doctrine, such that each of these classes\u0000of structures can be identified with the algebras for some such doctrine. We\u0000show that free algebras for LNL doctrines can be presented by a sequent\u0000calculus, and that every morphism of doctrines induces an adjunction between\u0000their 2-categories of algebras.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125879430","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":"Minimality Notions via Factorization Systems","authors":"Thorsten Wißmann","doi":"10.46298/lmcs-18(3:31)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:31)2022","url":null,"abstract":"For the minimization of state-based systems (i.e. the reduction of the number\u0000of states while retaining the system's semantics), there are two obvious\u0000aspects: removing unnecessary states of the system and merging redundant states\u0000in the system. In the present article, we relate the two minimization aspects\u0000on coalgebras by defining an abstract notion of minimality.\u0000 The abstract notions minimality and minimization live in a general category\u0000with a factorization system. We will find criteria on the category that ensure\u0000uniqueness, existence, and functoriality of the minimization aspects. The\u0000proofs of these results instantiate to those for reachability and observability\u0000minimization in the standard coalgebra literature. Finally, we will see how the\u0000two aspects of minimization interact and under which criteria they can be\u0000sequenced in any order, like in automata minimization.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115906587","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}
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