The visualization has become essential in many application areas. The finite graphs and automata undoubtedly belong to such areas. A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finitestate automaton. The visual perception of the structure properties of ...

We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263–1282] on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letter alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the...

In this paper we investigate from a statistical point of view the expected compression ratio between the size of a minimal Deterministic Finite Cover Automaton (DFCA) and the size of the minimal corresponding Determinitic Finite Automaton (DFA). Using sound statistical methods, we extend the experimental study done in [16], thus obtaining a much better picture of the compression power of DFCAs....

The visualization has become essential in many application areas. The finite graphs and automata undoubtedly belong to such areas. A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finitestate automaton. The visual perception of the structure properties of ...

The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and identities associated with finite automata. We show that the Conway identities and the identities associated with the members of a subclass Q of finite automa...

Traditional Fuzzy Automata are not sufficient to model complex real life applications such as biomedical systems where the inputs can be in terms of Fuzzy. Watson Crick Finite Automaton, which works on Double Stranded tapes was introduced a computational analyze DNA molecule for purpose. The concept Fuzziness and studied theory Automaton. thought an effective computing with problems having inco...

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 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...

It is shown that certain ascending HNN extensions of free abelian groups of finite rank, as well as various lamplighter groups, can be realized as automaton groups, i.e., can be given a self-similar structure. This includes the solvable Baumslag-Solitar groups BS(1, m), for m 6= ±1. In addition, it is shown that, for any relatively prime integers m, n ≥ 2, the pair of Baumslag-Solitar groups BS...

The symbolic automata toolkit lifts classical automata analysis to work modulo rich alphabet theories. It uses the power of stateof-the-art constraint solvers for automata analysis that is both expressive and efficient, even for automata over large finite alphabets. The toolkit supports analysis of finite symbolic automata and transducers over strings. It also handles transducers with registers...