In this paper, we define the notion of a bipolar general fuzzy automaton, then we construct some closure operators on the set of states of a bipolar general fuzzy automaton. Also, we construct some topologies on the set of states of a bipolar general fuzzy automaton. Then we obtain some relationships between them.

Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m, n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are con...

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.

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate swee...

Computations are developed for the synthesis of a finite state machine (FSM) embedded in a known FSM such that their combined behavior satisfies a co-Büchi specification (the solution must finally enter an acceptable set of states and stay there forever). The procedures for this are shown to be very similar to those used for regular (non-omega) automata, except for a final step in which a set o...

The field of finite tree automata provides fundamental notations and tools for reasoning about set of terms called regular or recognizable tree languages. We consider two kinds of analysis using regular tree languages, applied to logic programs. The first approach is to try to discover automatically a tree automaton from a logic program, approximating its minimal Herbrand model. In this case th...

We investigate the conversion of nondeterministic finite automata and context-free grammars into Parikh equivalent deterministic finite automata, from a descriptional complexity point of view. We prove that for each nondeterministic automaton with n states there exists a Parikh equivalent deterministic automaton with e √ n·lnn) states. Furthermore, this cost is tight. In contrast, if all the st...

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 ...

We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides unique decodability is given. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has at least exponentially...

Abs t r ac t . Approximate string matching is a sequential problem and therefore it is possible to solve it using finite automata. A nondeterministic finite automaton is constructed for string matching with k mismatches. It is shown, how "dynamic programming" and "shift-and" based algorithms simulate this nondeterministic finite automaton. The corresponding deterministic finite automaton have O...