{"title":"On the Relationship Between Matiyasevich's and Smorynski's Theorems","authors":"Agnieszka Peszek, A. Tyszka","doi":"10.7561/SACS.2019.1.101","DOIUrl":"https://doi.org/10.7561/SACS.2019.1.101","url":null,"abstract":"Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. Let R be a subring of Q with or without 1. By H_{10}(R), we denote the problem of whether there exists an algorithm which for any given Diophantine equation with integer coefficients, can decide whether or not the equation has a solution in R. We prove that a positive solution to H_{10}(R) implies that the set of all Diophantine equations with a finite number of solutions in R is recursively enumerable. We show the converse implication for every infinite set R subseteq Q such that there exist computable functions tau_1,tau_2:N to Z which satisfy (forall n in N tau_2(n) neq 0) wedge ({frac{tau_1(n)}{tau_2(n)}: n in N}=R). This implication for R=N guarantees that Smorynski's theorem follows from Matiyasevich's theorem. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have a rational solution is not recursive. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have only finitely many rational solutions is not recursively enumerable. These conjectures are equivalent by our results for R=Q.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131578576","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":"Program algebra for Turing-machine programs","authors":"J. Bergstra, K. Middelburg","doi":"10.7561/SACS.2019.2.113","DOIUrl":"https://doi.org/10.7561/SACS.2019.2.113","url":null,"abstract":"This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such behaviours and Turing tapes provided by an execution environment. This theory provides a setting for the development of theory in areas such as computability and computational complexity that distinguishes itself by offering the possibility of equational reasoning and being more general than the setting provided by a known version of the Turing-machine model of computation. The theory is essentially an instantiation of a parameterized algebraic theory which is the basis of a line of research in which issues relating to a wide variety of subjects from computer science have been rigorously investigated thinking in terms of instruction sequences.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132479894","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 Note on Congruences of Infinite Bounded Involution Lattices","authors":"C. Mureşan","doi":"10.7561/SACS.2021.1.51","DOIUrl":"https://doi.org/10.7561/SACS.2021.1.51","url":null,"abstract":"We prove that an infinite (bounded) involution lattice and even pseudo-Kleene algebra can have any number of congruences between 2 and its number of elements or equalling its number of subsets, regardless of whether it has as many ideals as elements or as many ideals as subsets. Furthermore, when they have at most as many congruences as elements, these involution lattices and even pseudo-Kleene algebras can be chosen such that all their lattice congruences preserve their involutions, so that they have as many congruences as their lattice reducts. Under the Generalized Continuum Hypothesis, this means that an infinite (bounded) involution lattice and even pseudo-Kleene algebra can have any number of congruences between 2 and its number of subsets, regardless of its number of ideals. Consequently, the same holds for antiortholattices, a class of paraorthomodular Brouwer-Zadeh lattices. Regarding the shapes of the congruence lattices of the lattice{ ordered algebras in question, it turns out that, as long as the number of congruences is not strictly larger than the number of elements, they can be isomorphic to any nonsingleton well-ordered set with a largest element of any of those cardinalities, provided its largest element is strictly join-irreducible in the case of bounded lattice-ordered algebras and, in the case of antiortholattices with at least 3 distinct elements, provided that the predecessor of the largest element of that well-ordered set is strictly join{irreducible, as well; of course, various constructions can be applied to these algebras to obtain congruence lattices with different structures without changing the cardinalities in question. We point out sufficient conditions for analogous results to hold in an arbitrary variety.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125850831","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":"The Theory of Finitely Supported Structures and Choice Forms","authors":"A. Alexandru","doi":"10.7561/sacs.2018.1.1","DOIUrl":"https://doi.org/10.7561/sacs.2018.1.1","url":null,"abstract":"The theory of finitely supported algebraic structures provides a first step in computing infinite algebraic structures that are finitely supported modulo certain atomic permutation actions. The motivation for developing such a theory comes from both mathematics (by modelling infinite algebraic structures, hierarchically defined by involving some basic elements called atoms, in a finitary manner, by analyzing their finite supports) and computer science (where finitely supported sets are used in various areas such as semantics foundation, automata theory, domain theory, proof theory and software verification). The results presented in this paper include the meta-theoretical presentation of finitely supported structures, the study of the consistency of choice principles (and of results requiring choice principles) within this framework, and the presentation of several connections with other topics.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128839242","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":"(Skew) Filters in Residuated Skew Lattices","authors":"R. Koohnavard, A. Saeid","doi":"10.7561/SACS.2018.1.115","DOIUrl":"https://doi.org/10.7561/SACS.2018.1.115","url":null,"abstract":"In this paper, we show the relationship between (skew) deductive system and (skew) filter in residuated skew lattices. It is shown that if a residuated skew lattice is conormal, then any skew deductive system is a skew filter under a condition and deductive system and skew deductive system are equivalent under some conditions too. It is investigated that in branchwise residuated skew lattice, filter, deductive system and skew deductive system are equivalent. We define some types of prime (skew) filters in residuated skew lattices and show the relationship between prime (skew) filters and residuated skew chains. It is proved that in prelinear residuated skew lattice any proper filter can be extended to a maximal, prime filter of type (I). The notion of the radical of a filter is defined and several characterizations of the radical of a filter are given. We show that in non conormal prelinear residuated skew lattice with element 0, infinitesimal elements are equal to intersection of all the maximal filters.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116166428","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}
E. Best, Raymond R. Devillers, U. Schlachter, Harro Wimmel
{"title":"Simultaneous Petri Net Synthesis","authors":"E. Best, Raymond R. Devillers, U. Schlachter, Harro Wimmel","doi":"10.7561/SACS.2018.2.199","DOIUrl":"https://doi.org/10.7561/SACS.2018.2.199","url":null,"abstract":"Petri net synthesis deals with the problem whether, given a labelled transition system TS , one can find a Petri net N with an initial markingM0 such that the reachability graph of (N,M0) is isomorphic to TS . This may be preceded by a pre-synthesis phase that will quickly reject ill-formed transition systems (and give structural reasons for the failure) and otherwise build data structures needed by the proper synthesis. The last phase proceeds by solving systems of linear inequalities, and may still fail but for less transparent reasons. In this paper, we consider an extended problem. A finite set of transition systems {TS 1, . . . ,TSm} shall be called simultaneously Petri net solvable if there is a single Petri netN with several initial markings {M01, . . . ,M0m}, such that for every i = 1, . . . ,m, the reachability graph of (N,M0i) is isomorphic to TS i. The focus will be on choice-free nets, that is, nets without structural choices, and we explore how previously published efficient algorithms for the pre-synthesis and proper synthesis of bounded and choice-free Petri nets can be generalised for the simultaneous pre-synthesis and synthesis of such multi-marked nets. At the same time, the choice-free pre-synthesis of a single transition system shall be strengthened by introducing new structural checks.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123783384","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}
Clément Bertrand, F. Peschanski, Hanna Klaudel, Matthieu Latapy
{"title":"Pattern Matching in Link Streams: Timed-Automata with Finite Memory","authors":"Clément Bertrand, F. Peschanski, Hanna Klaudel, Matthieu Latapy","doi":"10.7561/sacs.2018.2.161","DOIUrl":"https://doi.org/10.7561/sacs.2018.2.161","url":null,"abstract":"Link streams model the dynamics of interactions in complex distributed systems as sequences of links (interactions) occurring at a given time. Detecting patterns in such sequences is crucial for many applications but it raises several challenges. In particular, there is no generic approach for the specification and detection of link stream patterns in a way similar to regular expressions and automata for text patterns. To address this, we propose a novel automata framework integrating both timed constraints and finite memory together with a recognition algorithm. The algorithm uses structures similar to tokens in high-level Petri nets and includes non-determinism and concurrency. We illustrate the use of our framework in real-world cases and evaluate its practical performances.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"267 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114499798","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 Precise Characterisation of Step Traces and Their Concurrent Histories","authors":"R. Janicki, J. Kleijn, Lukasz Mikulski","doi":"10.7561/SACS.2018.2.237","DOIUrl":"https://doi.org/10.7561/SACS.2018.2.237","url":null,"abstract":"Step traces are an extension of Mazurkiewicz traces where each equivalence class (trace) consists of sequences of steps instead of sequences of atomic actions. Relations between the actions of the system are defined statically, as parameters of a concurrent step alphabet. By allowing only some of the possible relationships between actions, subclasses of step alphabets can be derived in a natural way. Properties of these classes can then be investigated in terms of invariant structures, i.e., the relational structures that represent the causal invariants that underlie the corresponding step traces. In this paper, we refine an earlier classification of subclasses of step alphabets and add eight new subclasses to this hierarchy. We divide these eight classes into three families on basis of the absence of a specific behavioural relation and then characterise the corresponding invariant structures.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128117667","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":"On Partition Metric Space, Index Function, and Data Compression","authors":"D. Simovici, Roman A. Sizov","doi":"10.7561/sacs.2018.1.141","DOIUrl":"https://doi.org/10.7561/sacs.2018.1.141","url":null,"abstract":"We discuss a metric structure on the set of partitions of a finite set induced by the Gini index and two applications of this metric: the identification of determining sets for index functions using techniques that originate in machine learning, and a data compression algorithm.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116426305","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":"High-Level Koutny Net","authors":"Gabriel Ciobanu","doi":"10.7561/SACS.2018.2.157","DOIUrl":"https://doi.org/10.7561/SACS.2018.2.157","url":null,"abstract":"This issue is dedicated to Professor Maciej Koutny for celebrating his 60th birthday, and consists of five contributions written by his friends and collaborators. This issue is dedicated to Professor Maciej Koutny for celebrating his 60th birthday. We celebrate Maciej not only for his 60th birthday, but also as an excellent researcher and a very good friend. There are five contributions written by his friends and collaborators. Each contribution has been carefully read through by at least two reviewers, and this improved the already high-quality articles. Many thanks to all of them, authors and reviewers! Maciej Koutny is a Professor of Computing Science in the School of Computing at Newcastle University. He received his MSc and PhD in Applied Mathematics from the Warsaw University of Technology. Then Maciej joined the Computing Laboratory of the Newcastle University in UK, where he is now the director of research in the School of Computing. Professor Maciej Koutny is a very active member of the Petri Net community, being currently the chair of the International Petri Net Steering Committee. He has investigated various semantics of Petri nets (causality semantics, step traces), synthesis and verification of Petri nets, model checking based on net unfoldings. Some of his work is devoted to the unification of Petri nets and process algebras, to the relationship between temporal logics and process algebras, as well as to modelling mobile and dynamic systems. He is also involved in scientific communities related to membrane computing and reaction systems representing novel models of computation inspired by the functioning of the living cells. He has been working on their","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128040909","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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