In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length ...

A cover-automaton A of a finite language L ⊆ Σ∗ is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic cover automaton of a finite language L usually has a smaller size than a minimal DFA that accept L. Thus, cover automata can be used to reduce the size of the representations of finite languages in practice. In thi...

We investigate several aspects of the multiple entry DFA’s. We consider their DFA conversion. Further, we show that they appear as minimal NFA’s for certain classes of languages. Finally, we deal with their decompositions into disjoint unions of automata with fewer states.

In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the prope...

We introduce a new geometric tool for analyzing groups of finite au-tomata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reproduc...

We propose a representation of simple conceptual graphs with binary conceptual relations, which is based on finite-state automata. The representation enables the calculation of injective projection as a two-stage process: off-line calculation of the computationally-intensive subsumption checks and encoding of the results as a minimal finite-state automaton, and run-time calculation by look-up i...

A deterministic finite automaton A is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton A to a particular one. We prove that it is a PSPACEcomplete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.