In this paper we prove that if the congruence lattice of an automaton A is finite then the endomorphism semigroup E(A) of A is finite. Moreover, if A is commutative then A is A-finite. We prove that if 3 ≤ |A| then a commutative automaton A is simple if and only if it is a cyclic permutation automaton of prime order. We also give some results concerning cyclic, strongly connected and strongly t...

It is well known that context-free parsing can be seen as the intersection of a contextfree language with a regular language (or, equivalently, the intersection of a context-free grammar with a finite-state automaton). The present article provides a practical efficient way to compute this intersection by converting the grammar into a special finite-state automaton (the GLR(0)-automaton) which i...

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 finite-state automaton. The visual perception of the structure properties of automata is an important goal. A synchronizing word of a deterministic automaton is a word in the alphabet of colors of its edges ...

in this note, by considering the notions of the intuitionistic general l-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{l}$, there exists a minimal intuitionistic general l-fuzzy automaton recognizing $mathcal{l}$.we prove that the minimal intuitionistic general l-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

We define a structurally unambiguous finite automaton (SUFA) to be a nondeterministic finite automaton (NFA) with one starting state q0 such that for all input strings w and for any state q, there is at most one path from q0 to q that consumes w. The definition of SUFA differs from the usual definition of an unambiguous finite automaton (UFA) in that the new definition is defined in terms of th...

The Aho-Corasick algorithm derives a failure deterministic finite automaton for finding matches of a finite set of keywords in a text. It has the minimum number of transitions needed for this task. The DFA-Homomorphic Algorithm (DHA) algorithm is more general, deriving from an arbitrary complete deterministic finite automaton a language-equivalent failure deterministic finite automaton. DHA tak...

We prove that every two-way nondeterministic finite automaton with n states has an equivalent one-way nondeterministic finite automaton with at most 2n n+1 states. We also show this bound is exact.

Given a finite alphabet Σ and a deterministic finite automaton on Σ, the problem of determining whether the language recognized by the automaton contains any pangram is NP-complete.