{"title":"Non-Deterministic Updates of Boolean Networks","authors":"Loïc Paulevé, Sylvain Sené","doi":"10.4230/OASIcs.AUTOMATA.2021.10","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.10","url":null,"abstract":"Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network evolves over time. Many of updating modes from the literature, including synchronous and asynchronous modes, can be defined as the composition of elementary deterministic configuration updates, i.e., by functions mapping configurations of the network. Nevertheless, alternative dynamics have been introduced using ad-hoc auxiliary objects, such as that resulting from binary projections of Memory Boolean networks, or that resulting from additional pseudo-states for Most Permissive Boolean networks. One may wonder whether these latter dynamics can still be classified as updating modes of finite Boolean networks, or belong to a different class of dynamical systems. In this paper, we study the extension of updating modes to the composition of non-deterministic updates, i.e., mapping sets of finite configurations. We show that the above dynamics can be expressed in this framework, enabling a better understanding of them as updating modes of Boolean networks. More generally, we argue that non-deterministic updates pave the way to a unifying framework for expressing complex updating modes, some of them enabling transitions that cannot be computed with elementary and non-elementary deterministic updates.","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"44 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":"126216962","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":"Reversible cellular automata in presence of noise rapidly forget everything","authors":"Siamak Taati","doi":"10.4230/OASIcs.AUTOMATA.2021.3","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.3","url":null,"abstract":"We consider reversible and surjective cellular automata perturbed with noise. We show that, in the presence of positive additive noise, the cellular automaton forgets all the information regarding its initial configuration exponentially fast. In particular, the state of a finite collection of cells with diameter n becomes indistinguishable from pure noise after O(log n) time steps. This highlights the seemingly unavoidable need for irreversibility in order to perform scalable reliable computation in the presence of noise.","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115650795","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":"Exploring Millions of 6-State FSSP Solutions: The Formal Notion of Local CA Simulation","authors":"T. Nguyen, Luidnel Maignan","doi":"10.1007/978-3-030-61588-8_1","DOIUrl":"https://doi.org/10.1007/978-3-030-61588-8_1","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124723677","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":"Complexity of Generic Limit Sets of Cellular Automata","authors":"Ilkka Törmä","doi":"10.1007/978-3-030-61588-8_10","DOIUrl":"https://doi.org/10.1007/978-3-030-61588-8_10","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":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123495568","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":"Enhancement of Automata with Jumping Modes","authors":"S. Fazekas, Kaito Hoshi, A. Yamamura","doi":"10.1007/978-3-030-20981-0_5","DOIUrl":"https://doi.org/10.1007/978-3-030-20981-0_5","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130239498","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":"Generic properties in some classes of automaton groups","authors":"Thibault Godin","doi":"10.1007/978-3-030-20981-0_7","DOIUrl":"https://doi.org/10.1007/978-3-030-20981-0_7","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125560346","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":"Bounding the Minimal Number of Generators of Groups and Monoids of Cellular Automata","authors":"Alonso Castillo-Ramirez, M. Sánchez-Álvarez","doi":"10.1007/978-3-030-20981-0_4","DOIUrl":"https://doi.org/10.1007/978-3-030-20981-0_4","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121712379","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":"Construction of Some Nonautomatic Sequences by Cellular Automata","authors":"Irène Marcovici, T. Stoll, Pierre-Adrien Tahay","doi":"10.1007/978-3-319-92675-9_9","DOIUrl":"https://doi.org/10.1007/978-3-319-92675-9_9","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129015186","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":"Glider Automorphisms on Some Shifts of Finite Type and a Finitary Ryan's Theorem","authors":"Johan Kopra","doi":"10.1007/978-3-319-92675-9_7","DOIUrl":"https://doi.org/10.1007/978-3-319-92675-9_7","url":null,"abstract":"","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132358327","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}