Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are ℤ-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type 𝔸r (for r ≥ 1), within the framework introduced in [Fundamenta Informaticae 184(1):49–82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.
{"title":"Coxeter Invariants for Non-negative Unit Forms of Dynkin Type 𝔸r","authors":"Jesús Arturo Jiménez González","doi":"10.3233/fi-222109","DOIUrl":"https://doi.org/10.3233/fi-222109","url":null,"abstract":"Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are ℤ-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type 𝔸r (for r ≥ 1), within the framework introduced in [Fundamenta Informaticae 184(1):49–82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"41 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73871881","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":"Preface [to A Mosaic of Computational Topics: from Classical to Novel, Special Issue Dedicated to Jetty Kleijn on the Occasion of Her 65th Birthday]","authors":"Beek M Ter, M. Koutny, G. Rozenberg","doi":"10.3233/FI-2020-1945","DOIUrl":"https://doi.org/10.3233/FI-2020-1945","url":null,"abstract":"","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3233/FI-2020-1945","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69903717","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":"Neighborhood Systems: Rough Set Approximations and Definability","authors":"Yu-Ru Syau, E. Lin, C. Liau","doi":"10.3233/FI-2018-1670","DOIUrl":"https://doi.org/10.3233/FI-2018-1670","url":null,"abstract":"","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"65 1","pages":"429-450"},"PeriodicalIF":0.8,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81505155","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}
In the early seventies, Shelah proposed a model-theoretic construction, nowadays called "iteration". This construction is an infinite replication in a tree-like manner where every vertex possesses its own copy of the original structure. Stupp proved that the decidability of the monadic second-order (MSO) theory is transferred from the original structure onto the iterated one. In its extended version discovered by Muchnik and introduced by Semenov, the iteration became popular in computer science logic thanks to a paper by Walukiewicz. Compared to the basic iteration, Muchnik’s iteration has an additional unary predicate which, in every copy, marks the vertex that is the clone of the possessor of the copy. A widely spread belief that this extension is crucial is formally confirmed in the paper. Two hierarchies of relational structures generated from finite structures by MSO interpretations and either Shelah-Stupp’s iteration or Muchnik’s iteration are compared. It turns out that the two hierarchies coincide at level 1. Every level of the latter hierarchy is closed under Shelah-Stupp’s interation. In particular, the former hierarchy collapses at level 1.
{"title":"Shelah-Stupp's Iteration and Muchnik's Iteration","authors":"D. Caucal, Teodor Knapik","doi":"10.3233/FI-2018-1667","DOIUrl":"https://doi.org/10.3233/FI-2018-1667","url":null,"abstract":"In the early seventies, Shelah proposed a model-theoretic construction, nowadays called \"iteration\". This construction is an infinite replication in a tree-like manner where every vertex possesses its own copy of the original structure. Stupp proved that the decidability of the monadic second-order (MSO) theory is transferred from the original structure onto the iterated one. In its extended version discovered by Muchnik and introduced by Semenov, the iteration became popular in computer science logic thanks to a paper by Walukiewicz. Compared to the basic iteration, Muchnik’s iteration has an additional unary predicate which, in every copy, marks the vertex that is the clone of the possessor of the copy. A widely spread belief that this extension is crucial is formally confirmed in the paper. Two hierarchies of relational structures generated from finite structures by MSO interpretations and either Shelah-Stupp’s iteration or Muchnik’s iteration are compared. It turns out that the two hierarchies coincide at level 1. Every level of the latter hierarchy is closed under Shelah-Stupp’s interation. In particular, the former hierarchy collapses at level 1.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"1 1","pages":"327-359"},"PeriodicalIF":0.8,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83392464","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}
DNA strand replacement technology has the advantages of simple operation which makes it becomes a common method of DNA computing. A four bit binary number Complementer based on two-domain DNA strand displacement is proposed in this paper. It implements the function of converting binary code into complement code. Simulation experiment based on Visual DSD software is carried out. The simulation results show the correctness and feasibility of the logic model of the Complementer, and it makes useful exploration for further expanding the application of molecular logic circuit.
{"title":"Logic Operation Model of the Complementer Based on Two-domain DNA Strand Displacement","authors":"Wendan Xie, Changjun Zhou, Hui Lv, Qiang Zhang","doi":"10.3233/FI-2019-1767","DOIUrl":"https://doi.org/10.3233/FI-2019-1767","url":null,"abstract":"DNA strand replacement technology has the advantages of simple operation which makes it becomes a common method of DNA computing. A four bit binary number Complementer based on two-domain DNA strand displacement is proposed in this paper. It implements the function of converting binary code into complement code. Simulation experiment based on Visual DSD software is carried out. The simulation results show the correctness and feasibility of the logic model of the Complementer, and it makes useful exploration for further expanding the application of molecular logic circuit.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"1 1","pages":"1-8"},"PeriodicalIF":0.8,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3233/FI-2019-1767","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44693572","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}
J. Cassaigne, J. Karhumäki, S. Puzynina, Markus A. Whiteland
Two words u and v are said to be k-abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v. We study some combinatorial properties of k-abelian equivalence classes. Our starting point is a characterization of k-abelian equivalence by rewriting, so-called k-switching. We show that the set of lexicographically least representatives of equivalence classes is a regular language. From this we infer that the sequence of the numbers of equivalence classes is $$mathbb {N}$$-rational. We also show that the set of words defining k-abelian singleton classes is regular.
{"title":"k-Abelian Equivalence and Rationality","authors":"J. Cassaigne, J. Karhumäki, S. Puzynina, Markus A. Whiteland","doi":"10.3233/FI-2017-1553","DOIUrl":"https://doi.org/10.3233/FI-2017-1553","url":null,"abstract":"Two words u and v are said to be k-abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v. We study some combinatorial properties of k-abelian equivalence classes. Our starting point is a characterization of k-abelian equivalence by rewriting, so-called k-switching. We show that the set of lexicographically least representatives of equivalence classes is a regular language. From this we infer that the sequence of the numbers of equivalence classes is $$mathbb {N}$$-rational. We also show that the set of words defining k-abelian singleton classes is regular.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"15 1","pages":"77-88"},"PeriodicalIF":0.8,"publicationDate":"2016-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89752767","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}
We consider computational complexity of problems related to partial word au- tomata. Roughly speaking, a partial word is a word in which some positions are unspecified, and a partial word automaton is a finite automaton that accepts a partial word language— here the unspecified positions in the word are represented by a "hole" symbol ⋄. A partial word language Lcan be transformed into an ordinary language L by using a ⋄-substitution. In particular, we investigate the complexity of the compression or minimization problem for partial word automata, which is known to be NP-hard. We improve on the previously known complexity on this problem, by showing PSPACE-completeness. In fact, it turns out that almost all problems related to partial word automata, such as, e.g., equivalence and universality, are already PSPACE-complete. Moreover, we also study these problems under the further restriction that the involved automata accept only finite languages. In this case, the complexity of the studied problems drop from PSPACE-completeness down to coNP-hardness and containment in § P depending on the problem investigated.
{"title":"On the Computational Complexity of Partial Word Automata Problems","authors":"M. Holzer, Sebastian Jakobi, Matthias Wendlandt","doi":"10.3233/FI-2016-1435","DOIUrl":"https://doi.org/10.3233/FI-2016-1435","url":null,"abstract":"We consider computational complexity of problems related to partial word au- tomata. Roughly speaking, a partial word is a word in which some positions are unspecified, and a partial word automaton is a finite automaton that accepts a partial word language— here the unspecified positions in the word are represented by a \"hole\" symbol ⋄. A partial word language Lcan be transformed into an ordinary language L by using a ⋄-substitution. In particular, we investigate the complexity of the compression or minimization problem for partial word automata, which is known to be NP-hard. We improve on the previously known complexity on this problem, by showing PSPACE-completeness. In fact, it turns out that almost all problems related to partial word automata, such as, e.g., equivalence and universality, are already PSPACE-complete. Moreover, we also study these problems under the further restriction that the involved automata accept only finite languages. In this case, the complexity of the studied problems drop from PSPACE-completeness down to coNP-hardness and containment in § P depending on the problem investigated.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"98 1","pages":"131-146"},"PeriodicalIF":0.8,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73066650","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}
J. Bomanson, M. Gebser, T. Janhunen, B. Kaufmann, Torsten Schaub
Acyclicity constraints are prevalent in knowledge representation and, in particular, applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related with recursive structures. The implementation, obtained as an extension to the state-of-the-art answer set solver clasp, provides a unique combination of traditional unfounded set checking with acyclicity propagation.
{"title":"Answer Set Programming Modulo Acyclicity","authors":"J. Bomanson, M. Gebser, T. Janhunen, B. Kaufmann, Torsten Schaub","doi":"10.3233/FI-2016-1398","DOIUrl":"https://doi.org/10.3233/FI-2016-1398","url":null,"abstract":"Acyclicity constraints are prevalent in knowledge representation and, in particular, applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related with recursive structures. The implementation, obtained as an extension to the state-of-the-art answer set solver clasp, provides a unique combination of traditional unfounded set checking with acyclicity propagation.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":"68 1","pages":"143-150"},"PeriodicalIF":0.8,"publicationDate":"2015-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77777049","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}
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