Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible languages, respectively. The existence of k-reversible languages which are not (k−1)-reversible is known, for each k > 1. This gives an infinite hierarchy o...

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...

The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for computing the edit-distance between a string and an arbitrary weighted automaton over the tropical semiring, or an unambiguous weighted automaton over an arbitrary...

A two-way finite automaton is sweeping if its input head can change direction only on the end-markers. For each n ≥ 2, we exhibit a problem that can be solved by a O(n)-state sweeping LasVegas automaton, but needs 2 states on every sweeping deterministic automaton.

In this paper we consider non-deterministic finite Rabin–Scott’s automata. We obtain some properties for the basis automaton, which is, like automaton of canonical form, an invariant of a given regular language. We obtain also a new algorithm of constructing the basis automaton for a given regular language.

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

We describe an automata-theoretic approach to the automatic verification of finite-state programs. The basic idea underlying this approach is that for any temporal formula we can construct an alternating automaton that accepts precisely the computations that satisfy the formula. For linear temporal logics the automaton runs on infinite words while for branching temporal logics the automaton run...

We present examples where theorems on complexity of computation are proved using methods in algorithmic information theory. The first example is a non-effective construction of a language for which the size of any deterministic finite automaton exceeds the size of a probabilistic finite automaton with a bounded error exponentially. The second example refers to frequency computation. Frequency c...

The problem of analyzing the finite time behavior of learning automata is considered. This problem involves the finite time analysis of the learning algorithm used by the learning automaton and is important in determining the rate of convergence of the automaton. In this paper, a general framework for analyzing the finite time behavior of the automaton learning algorithms is proposed. Using thi...

The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device with a finite number of internal states. Section ...