{"title":"Conjunctive Grammars, Cellular Automata and Logic","authors":"Théo Grente, E. Grandjean","doi":"10.4230/OASIcs.AUTOMATA.2021.8","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.8","url":null,"abstract":"The expressive power of the class Conj of conjunctive languages, i.e. languages generated by the conjunctive grammars of Okhotin, is largely unknown, while its restriction LinConj to linear conjunctive grammars equals the class of languages recognized by real-time one-dimensional one-way cellular automata. We prove two weakened versions of the open question Conj ⊆? RealTime1CA, where RealTime1CA is the class of languages recognized by real-time one-dimensional two-way cellular automata: 1. it is true for unary languages; 2. Conj ⊆ RealTime2OCA, i.e. any conjunctive language is recognized by a real-time two-dimensional one-way cellular automaton. Interestingly, we express the rules of a conjunctive grammar in two Horn logics, which exactly characterize the complexity classes RealTime1CA and RealTime2OCA. 2012 ACM Subject Classification Theory of computation → Complexity theory and logic; Theory of computation → Formal languages and automata theory","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128430948","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":"Dynamical Properties of Disjunctive Boolean Networks (Invited Talk)","authors":"M. Gadouleau","doi":"10.4230/OASIcs.AUTOMATA.2021.1","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.1","url":null,"abstract":"A Boolean network is a mapping $f :{0,1}^n to {0,1}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current configuration of states. In this paper, we are interested in disjunctive networks, where each local function is simply the disjunction of a set of variables. As such, this network is somewhat homogeneous, though the number of variables may vary from entity to entity, thus yielding a generalised cellular automaton. The aim of this paper is to review some of the main results, derive some additional fundamental results, and highlight some open problems, on the dynamics of disjunctive networks. We first review the different defining characteristics of disjunctive networks and several ways of representing them using graphs, Boolean matrices, or binary relations. We then focus on three dynamical properties of disjunctive networks: their image points, their periodic points, and their fixed points. For each class of points, we review how they can be characterised and study how many they could be. The paper finishes with different avenues for future work on the dynamics of disjunctive networks and how to generalise them.","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122046310","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 Characterization of Amenable Groups by Besicovitch Pseudodistances","authors":"Silvio Capobianco, Pierre Guillon, C. Noûs","doi":"10.1007/978-3-030-61588-8_8","DOIUrl":"https://doi.org/10.1007/978-3-030-61588-8_8","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114647168","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":"Regular Languages: To Finite Automata and Beyond (Invited Talk)","authors":"Luca Prigioniero","doi":"10.4230/OASIcs.AUTOMATA.2021.2","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.2","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132311500","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":"State-Based Opacity of Real-Time Automata","authors":"Kuize Zhang","doi":"10.4230/OASIcs.AUTOMATA.2021.12","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.12","url":null,"abstract":"State-based opacity is a special type of opacity as a confidentiality property, which describes whether an external intruder cannot make for sure whether secret states of a system have been visited by observing generated outputs, given that the intruder knows complete knowledge of the system’s structure but can only see generated outputs. When the time of visiting secret states is specified as the initial time, the current time, any past time, and at most K steps prior to the current time, the notions of state-based opacity can be formulated as initial-state opacity, current-state opacity, infinite-step opacity, and K-step opacity, respectively. In this paper, we formulate the four versions of opacity for real-time automata which are a widely-used model of real-time systems, and give 2-EXPTIME verification algorithms for the four notions by defining appropriate notions of observer and reverse observer for real-time automata that are computable in 2-EXPTIME. 2012 ACM Subject Classification Theory of computation Ñ Timed and hybrid models; Security and privacy Ñ Formal security models","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121702936","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":"Cellular Automata and Discrete Complex Systems - 23rd IFIP WG 1.5 International Workshop, AUTOMATA 2017, Milan, Italy, June 7-9, 2017, Proceedings","authors":"A. Dennunzio, E. Formenti, L. Manzoni, A. Porreca","doi":"10.1007/978-3-319-58631-1","DOIUrl":"https://doi.org/10.1007/978-3-319-58631-1","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125020705","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}