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Merging States and Synchronization Problem

Roman A.

Schedae Informaticae

2006

Vol. 15

95-108

In this paper we introduce the notion of merging states and merging systems and we use it for the classification of finite de- terministic automata without initial and final states. We investigate the dependencies between the structure of an automaton described by merging systems and maximal lengths of minimal synchronizing words for automata which structures belong to the given class of merging sys- tems. Numerical results for certain classes of automata are presented. We also give some properties of merging systems themselves. The work is motivated by the famous, unsolved Cerny Conjecture. The aim of this paper is to propose the use of merging systems in the research on the Conjecture.