Semisimple Synchronizing Automata and the Wedderburn-Artin Theory

Semisimple Synchronizing Automata and the Wedderburn-Artin Theory

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

On a Wedderburn-artin Structure Theory of a Potent Semiring.

A bound for the shortest reset words for semisimple synchronizing automata via the packing number

We show that if a semisimple synchronizing automaton with $n$ states has a minimal reachable non-unary subset of cardinality $r\ge 2$, then there is a reset word of length at most $(n-1)D(2,r,n)$, where $D(2,r,n)$ is the $2$-packing number for families of $r$-subsets of $[1,n]$.

Synchronizing groups and automata

Pin showed that every p-state automaton (p a prime) containing a cyclic permutation and a non-permutation has a synchronizing word of length at most (p− 1). In this paper we consider permutation automata with the property that adding any non-permutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words. In particular, we show that permutation grou...