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Author Lobos, F.; Goles, E.; Ruivo, E.L.P.; de Oliveira, P.P.B.; Montealegre, P. url  openurl
  Title Mining a Class of Decision Problems for One-dimensional Cellular Automata Type
  Year 2018 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.  
  Volume 13 Issue 5-6 Pages 393-405  
  Keywords One-dimensional cellular automata; decision problems; density classification; parity problem  
  Abstract Cellular automata are locally defined, homogeneous dynamical systems, discrete in space, time and state variables. Within the context of one-dimensional, binary, cellular automata operating on cyclic configurations of odd length, we consider the general decision problem: if the initial configuration satisfies a given property, the lattice should converge to the fixed-point of all 1s ((1) over right arrow), or to (0) over right arrow, otherwise. Two problems in this category have been widely studied in the literature, the parity problem [1] and the density classification task [4]. We are interested in determining all cellular automata rules with neighborhood sizes of 2, 3, 4 and 5 cells (i.e., radius r of 0.5, 1, 1.5 and 2.5) that solve decision problems of the previous type. We have demonstrated a theorem that, for any given rule in those spaces, ensures the non existence of fixed points other than (0) over right arrow and (1) over right arrow for configurations of size larger than 2(2r), provided that the rule does not support different fixed points for any configuration with size smaller than or equal to 2(2r). In addition, we have a proposition that ensures the convergence to only (0) over right arrow or (1) over right arrow of any initial configuration, if the rule complies with given conditions. By means of theoretical and computational approaches, we determined that: for the rule spaces defined by radius 0.5 and r = 1, only 1 and 2 rules, respectively, converge to (1) over right arrow or (0) over right arrow, to any initial configuration, and both recognize the same language, and for the rule space defined by radius r = 1.5, 40 rules satisfy this condition and recognize 4 different languages. Finally, for the radius 2 space, out of the 4,294,967,296 different rules, we were able to significantly filter it out, down to 40,941 candidate rules. We hope such an extensive mining should unveil new decision problems of the type widely studied in the literature.  
  Address [Lobos, Fabiola; Goles, Eric; Montealegre, Pedro] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Ave Diagonal Torres 2640, Santiago, Chile, Email: pp.balbi@gmail.com  
  Corporate Author Thesis  
  Publisher Old City Publishing Inc Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1557-5969 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000449762900002 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 931  
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Author Perrot, K.; Montalva-Medel, M.; de Oliveira, P.P.B.; Ruivo, E.L.P. doi  openurl
  Title Maximum sensitivity to update schedules of elementary cellular automata over periodic configurations Type
  Year 2020 Publication Natural Computing Abbreviated Journal Nat. Comput.  
  Volume 19 Issue 1 Pages 51-90  
  Keywords Synchronism sensitivity; Elementary cellular automata; Update digraph  
  Abstract This work is a thoughtful extension of the ideas sketched in Montalva et al. (AUTOMATA 2017 exploratory papers proceedings, 2017), aiming at classifying elementary cellular automata (ECA) according to their maximal one-step sensitivity to changes in the schedule of cells update. It provides a complete classification of the ECA rule space for all period sizes n[ 9 and, together with the classification for all period sizes n <= 9 presented in Montalva et al. (Chaos Solitons Fractals 113:209-220, 2018), closes this problem and opens further questionings. Most of the 256 ECA rule's sensitivity is proved or disproved to be maximum thanks to an automatic application of basic methods. We formalize meticulous case disjunctions that lead to the results, and patch failing cases for some rules with simple arguments. This gives new insights on the dynamics of ECA rules depending on the proof method employed, as for the last rules 45 and 105 requiring o0011THORN induction patterns.  
  Address [Perrot, Kevin] Univ, Aix Marseille Univ.,Toulon,CNRS,UMR 7020, Marseille, France, Email: kevin.perrot@lis-lab.fr  
  Corporate Author Thesis  
  Publisher Springer Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1567-7818 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000517129300006 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1162  
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Author Ruivo, E.L.P.; de Oliveira, P.P.B.; Lobos, F.; Goles, E. pdf  doi
openurl 
  Title Shift-equivalence of k-ary, one-dimensional cellular automata rules Type
  Year 2018 Publication Communications In Nonlinear Science And Numerical Simulation Abbreviated Journal Commun. Nonlinear Sci. Numer. Simul.  
  Volume 63 Issue Pages 280-291  
  Keywords One-dimensional cellular automata; Dynamical behaviour; Dynamical equivalence; Shift equivalence  
  Abstract Cellular automata are locally-defined, synchronous, homogeneous, fully discrete dynamical systems. In spite of their typically simple local behaviour, many are capable of showing complex emergent behaviour. When looking at their time-evolution, one may be interested in studying their qualitative dynamical behaviour. One way to group rules that display the same qualitative behaviour is by defining symmetries that map rules to others, the simplest way being by means of permutations in the set of state variables and reflections in their neighbourhood definitions, therefore defining equivalence classes. Here, we introduce the notion of shift-equivalence as another kind of symmetry, now relative to the concept of translation. After defining the notion and showing it indeed defines an equivalence relation, we extend the usual characterisation of dynamical equivalence and use it to partition some specific binary cellular automata rule spaces. Finally, we give a characterisation of the class of shift-equivalent rules in terms of the local transition functions of the cellular automata in the class, by providing an algorithm to compute the members of the class, for any k-ary, one-dimensional rule. (C) 2018 Elsevier B.V. All rights reserved.  
  Address [Ruivo, Eurico L. P.; de Oliveira, Pedro P. B.] Univ Presbiteriana Mackenzie, Fac Comp & Informat, Rua Consolacao 896, BR-01302907 Sao Paulo, SP, Brazil, Email: eurico.ruivo@mackenzie.br  
  Corporate Author Thesis  
  Publisher Elsevier Science Bv Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1007-5704 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000432822500022 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 870  
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Author Ruivo, E.L.P.; de Oliveira, P.P.B.; Montalva-Medel, M.; Perrot, K. doi  openurl
  Title Maximum sensitivity to update schedules of elementary cellular automata over infinite configurations Type
  Year 2020 Publication Information and Computation Abbreviated Journal Inf. Comput.  
  Volume 274 Issue SI Pages 104538  
  Keywords  
  Abstract Cellular automata are discrete dynamical systems with locally defined behaviour, well known as simple models of complex systems. Classically, their dynamics derive from synchronously iterated rules over finite or infinite configurations; however, since for many natural systems to be modelled, asynchrony seems more plausible, asynchronous iteration of the rules has gained a considerable attention in recent years. One question in this context is how changing the update schedule of rule applications affects the global behaviour of the system. In particular, previous works addressed the notion of maximum sensitivity to changes in the update schemes for finite lattices. Here, we extend the notion to infinite lattices, and classify elementary cellular automata space according to such a property.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0890-5401 ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1122  
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Author Ruivo, E.L.P.; Montalva-Medel, M.; de Oliveira, P.P.B.; Perrot, K. pdf  doi
openurl 
  Title Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates Type
  Year 2018 Publication Chaos Solitons & Fractals Abbreviated Journal Chaos Solitons Fractals  
  Volume 113 Issue Pages 209-220  
  Keywords Cellular automaton; Asynchronous update; Update digraph; Discrete dynamics; One-step maximum sensitivity  
  Abstract Cellular automata are fully-discrete dynamical systems with global behaviour depending upon their locally specified state transitions. They have been extensively studied as models of complex systems as well as objects of mathematical and computational interest. Classically, the local rule of a cellular automaton is iterated synchronously over the entire configuration. However, the question of how asynchronous updates change the behaviour of a cellular automaton has become a major issue in recent years. Here, we analyse the elementary cellular automata rule space in terms of how many different one-step trajectories a rule would entail when taking into account all possible deterministic ways of updating the rule, for one time step, over all possible initial configurations. More precisely, we provide a characterisation of the elementary cellular automata, by means of their one-step maximum sensitivity to all possible update schedules, that is, the property that any change in the update schedule causes the rule's one-step trajectories also to change after one iteration. Although the one-step maximum sensitivity does not imply that the remainder of the time-evolutions will be distinct, it is a necessary condition for that. (C) 2018 Elsevier Ltd. All rights reserved.  
  Address [Ruivo, Eurico L. P.; de Oliveira, Pedro P. B.] Univ Presbiteriana Mackenzie, Fac Comp & Informat, Sao Paulo, SP, Brazil, Email: eurico.ruivo@mackenzie.br  
  Corporate Author Thesis  
  Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0960-0779 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000442101600024 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 910  
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