Finite semigroups, feedback, and the Letichevsky criteria on non-empty words in finite automata

Automata and semigroups recognizing infinite words

This paper is a survey on the algebraic approach to the theory of automata accepting infinite words. We discuss the various acceptance modes (Büchi automata, Muller automata, transition automata, weak recognition by a finite semigroup, ω-semigroups) and prove their equivalence. We also give two algebraic proofs of McNaughton’s theorem on the equivalence between Büchi and Muller automata. Finall...

Decidability and Tameness in the Theory of Finite Semigroups

Large Aperiodic Semigroups

The syntactic complexity of a regular language is the size of its syntactic semigroup. This semigroup is isomorphic to the transition semigroup of the minimal deterministic finite automaton accepting the language, that is, to the semigroup generated by transformations induced by non-empty words on the set of states of the automaton. In this paper we search for the largest syntactic semigroup of...

Decision and Separability Problems for Baumslag-Solitar Semigroups

We show that the semigroups Sk,` having semigroup presentations 〈a, b : abk = b`a〉 are residually finite and finitely separable. Generally, these semigroups have finite separating images which are finite groups and other finite separating images which are semigroups of order-increasing transformations on a finite partially ordered set. These semigroups thus have vastly different residual and se...

Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)

This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...