In this paper, we introduce and study notions like state-\linebreak distinguishability, input-distinguishability and output completeness of states of a crisp deterministic fuzzy automaton. We show that for each crisp deterministic fuzzy automaton there corresponds a unique (up to isomorphism), equivalent distinguished crisp deterministic fuzzy automaton. Finally, we introduce two axioms related...

In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are rev...

This work considers weak deterministic Büchi automata reading encodings of non-negative d-vectors of reals in a fixed base. A saturated language is a language which contains all encoding of elements belonging to a set of d-vectors of reals. A Real Vector Automaton is an automaton which recognizes a saturated language. It is explained how to decide in quasi-linear time whether a minimal weak det...

The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1,L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation prob...

The only presently known normal form for a regular language L ∈ Reg is its Minimal Deterministic Automaton MDA(L). We show that a regular language is also characterized by a finite dimension dim(L), which is always smaller than the number |MDA(L)| of states, and often exponentially so. The dimension is also the minimal number of states of all Nondeterministic Xor Automaton (NXA) which accept th...

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...

A réversible automaton is a finite automaton in which each letter induces a partial one-to-one map from the set of states into itself. We solve the following problem proposed by Pin. Given an alphabet A, does there exist a séquence of languages Kn on A which can be accepted by a réversible automaton, and such that the number of states of the minimal automaton of Kn is in O(n), while the minimal...

Mikhail J. Atallah t Purdue University Given two strings T = at ... an and P = hI .. .hm over an alphabet E, the problem of testing whether P occurs as a subsequence of T is trivially solved in linear time. It is also known that a simple D(nlog lEI) time preprocessing ofT makes it easy to decide subsequently for any P and in at most IPJIog lEI character comparisons, whether P is a subsequence o...