Abstract In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties transformations of Muller automata. We present first practical implementation ACD in two different tools, Owl Spot, adapt it framework Emerson-Lei automata, i.e., $$\omega $$ ω -automata...

in the last decade, cellular automata models have been widely used for simulation spatial phenomena; however, exact nature of these models have been lead to various limitations for essential simulation of these phenomena. in this research, traditional cellular automata models have been developed through fuzzy theory, in which, transition rules are expressed based on fuzzy logic control methodol...

Let C be a oneor two-sided Kazhdan–Lusztig cell in a Coxeter group (W,S), and let Reduced(C) be the set of reduced expressions of all w ∈ C, regarded as a language over the alphabet S. Casselman has conjectured that Reduced(C) is regular. In this paper we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Ca...

Fix a finite set S ⊂ GL(k,Z). Denote by an the number of products of matrices in S of length n that are equal to 1. We show that the sequence {an} is not always P-recursive. This answers a question of Kontsevich.

It is a well-known fact that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal’s triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular automata is a much explored topic, but virtually all of the results revolve around a special class of automata, whose main features include irreversi...

In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic.

If M = ZD, and B is a finite (nonabelian) group, then B is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation G : B−→ B which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of B. We characterize when MCA are group endomorphisms of B, and show that MCA on B inherit a natural structure theory from t...

We construct a family of automata with n states, n ≥ 4, acting on a rooted binary tree that generate the free products of cyclic groups of order 2.

A class of additive cellular automata (ACA) on a finite group is defined by an index-group g and a finite field Fp for a prime modulus p [1]. This paper deals mainly with ACA on infinite commutative groups and direct products of them with some non commutative p-groups. It appears that for all abelian groups, the rules and initial states with finite supports define behaviors which being restrict...