Exploring Millions of 6-State FSSP Solutions: the Formal Notion of Local CA Simulation

Exploration de millions de solutions FSSP: la notion formelle de simulation locale d'automate cellulaire

Tien Thao Nguyen (1) , Luidnel Maignan (1)

1 LACL - Laboratoire d'Algorithmique Complexité et Logique

In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. This notion is used to explore solutions of the Firing Squad Synchronization Problem that are minimal both in time (2n − 2 for n cells) and, up to current knowledge, also in states (6 states). While only one such solution was proposed by Mazoyer since 1987, 718 new solutions have been generated by Clergue, Verel and Formenti in 2018 with a cluster of machines. We show here that, starting from existing solutions, it is possible to generate millions of such solutions using local simulations using a single common personal computer.

Mots clés: Cellular automata; Automata minimization; Firing squad synchronization problem.

Domaines: Informatique [cs]; Automates cellulaires et gaz sur réseau [nlin.CG]; Calcul parallèle, distribué et partagé [cs.DC]; Système multi-agents [cs.MA]; Théorie et langage formel [cs.FL]

Tien Thao Nguyen, Luidnel Maignan. Exploring Millions of 6-State FSSP Solutions: the Formal Notion of Local CA Simulation. 26th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Aug 2020, Stockholm, Sweden. pp.1-13, ⟨10.1007/978-3-030-61588-8_1⟩. ⟨hal-02605712⟩