Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments in quantum information theory may have appropriate formalizations in the automaton context. 1 Physical connections Physics and computer science share common i...

I explore the idea of simplicity as a belief-selection criterion in games. A pair of strategies in finite-automata representation (s1, s2) is a “Simple Nash Equilibrium” (SINE) if: (1) sj is a best-reply to si ; (2) every automaton for player j, which generates the same path as sj (given si), has at least as many states as sj . I apply SINE to a bilateral concession game and show that it captur...

We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in a local manner (called local orientation) so that the automaton is able to distinguish them. Precisely, th...

We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective if and only if it is preinjective. Pre-Injectivity means that two global configurations that differ at most on a finite subset and have the ...

We present the result of the article [1], in which a theoretical analysis of extension of the finite automaton built on DNA (introduced by the Shapiro team) to an arbitrary number of states and symbols is given. The Shapiro automaton action is based on cyclic cutting and ligating of DNA molecules. Its distinctive features included the fact that it was programmable (it means we may choose arbitr...

In this paper, we propose a regular expression matching circuit based on a decomposed automaton. To implement a regular expression matching circuit, first, we convert regular expressions into a non-deterministic finite automaton (NFA). Then, to reduce the number of states, we convert the NFA into a modular non-deterministic finite automaton with unbounded string transition (MNFAU). Next, to rea...

A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with n states has a synchronizing word of length at most (n− 1). We introduce the notion of aperiodically 1−contracting automata and prove that in these automata all subsets of the state set are reachable, so ...

A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an NP-complete problem. We prove that it remains NP-complete even if restricted to Eulerian automata with binary alphabets, as it has been conjectured by Martyu...

A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with n states has a synchronizing word of length at most (n− 1)2. We introduce the notion of aperiodically 1-contracting automata and prove that in these automata all subsets of the state set are reachable, so...