Showing papers on "ω-automaton published in 1972"

Endliche Automaten und Zufallsfolgen

Abstract: We consider the behaviour of finite automata on infinite binary sequences and study the class of random tests which can be carried out by finite automata. We give several equivalent characterizations of those infinite binary sequences which are random relative to finite automata. These characterizations are based on the concepts of selection rules, martingales and invariance properties defined by finite automata.

Finite automata and Burnside's problem for periodic groups

Abstract: New examples of infinite periodic finitely-generated groups are constructed. The elements of the groups are mappings of a set of words in an alphabet X into itself induced by finite Mealy automata. Estimates are given of the number of states and diagrams of the automata realizing the generating elements of the groups. There are three items in the literature cited.

The emptiness problem for automata on infinite trees

Abstract: The purpose of this paper is to give an alternative proof to the decidability of the emptiness problem for tree automata, as shown in Rabin4. The proof reduces the emptiness problem for automata on infinite trees to that for automata on finite trees, by showing that any automata definable set of infinite trees must contain a finitely-generable tree.

Some Classes of Multi-Input Automata

Abstract: The development of automata as control and simulation devices was prompted by problems of control of plants with unknown internal structure, as well as by problems of control and simulation of the economy and of many physiological processes. In describing the class of G-automata with many inputs, Sragovich [1] has cited earlier automata models with many inputs, whose generalization led to the G-type automaton. The various classes of such automata, represent both mathematical and applied interest, in that their analysis should reveal the necessary and/or sufficient conditions for their optimal behavior in various environments, and perhaps will even show which of the classes is “better.”

A medvedev characterization of sets recognized by generalized finite automata

Abstract: 1. In [2], I. T. Medvedev characterizes the regular events of S. C. Kleene [1] as the smallest class of sets containing a particular class of four primitive events and closed under a class of five primitive operations. In this paper the analogues of Medvedev's primitives are defined for terms (trees) over a ranked alphabet. It is then proved that the class of sets of terms generated by these primitives is identical with the regular sets of terms of J. W. Thatcher and J. B. Wright [3] which arise in generalized finite automata theory. In the process of extending Medvedev's results to trees it was discovered that, whereas his method required a minimum of four primitive sets and five primitive operations, the number of primitive events and primitive operations can each be diminished by one. In addition, involving the semigroup of an automaton has been avoided as it is unnecessary. Since the article of Medvedev is inaccessible to many readers for a variety of reasons, we include, in Section 3, a shorter direct proof of his result using a smaller class of primitives. The reader who is interested only in this result may omit Section 2

Some results in tree automata

Abstract: The following three results concerning tree automata are presented in this paper. (1) Rounds has presented the following open problem: For every recognizable setR, can we construct a deterministic finite-state transformation recognizingR? We show that this is not possible, in fact, even for a local set. However, the following is true: For every recognizable setR there is an inverse projectionR′ effectively obtained such thatR′ is recognized by a deterministic finite-state transformation. (2) Martin and Vere in their study of tree automata leave open the question of whether Generalized Syntax Directed Transductions (GSDT's) are closed under Arden's transformation or Greibach's transformation, and conjecture that they are not. We prove that this conjecture is true. It is also shown that GSDT's are not closed under transformation to LR(k) grammars. (3) Peters and Ritchie have shown that if, in a grammar where the generative rules are context-free, there are “recognition” rules which are context-sensitive, the language recognized is still context-free. A tree-automata-oriented proof is given by Rounds. We show that a similar result holds also for right linear grammars, i.e., if the generative rules are right linear, then using context-sensitive rules for “recognition”, one can still recognize only regular languages. Some other related results concerning context-sensitive extensions of subclasses of context-free languages are also presented.

A Programmer's View of Automata

Abstract: The purpose of this discussion is to introduce the Computer Scientist to the concepts, definitions, notation and ideas of finite automata theory and to suggest how these ideas might relate to some of the other fields of Computer Science. Many of the ideas presented will be familiar to computer programmers, although they might not be immediately recognizable, for it is the precise nature of mathematics that renders these concepts tractable to investigation. Since understanding of the basic concepts is the purpose of this discussion, more emphasis will be placed on definitions and examples than on theorems and proofs. The principal benefit of the study of finite automata to the computer programmer is not in theories and theorems, but is rather in the insight and understanding it can contribute to many programming problems; specifically, in determining the underlying structure of the problem and in establishing how this structure is modified as the computation progresses.

Semigroups of Automata

Abstract: : A new means of associating a semigroup with an automaton is presented. Some preliminary results are reported that suggest that this new class of semigroups more faithfully carries the structure of the original automaton than the classical semigroup approach does. (Author)

On two-state isolated probabilistic automata

Abstract: In this paper we generalize and extend Yasui and Yajima's results on two-state two-symbol probabilistic automata to the two-state multisymbol case We use a slightly different notion of isolated probabilistic automata independent of the initial distribution An algorithm is derived to synthesize such automata Finally we show the existence of a regular language accepted by some completely isolated probabilistic automaton

Der programmierbare endliche automat

Abstract: The paper deals with finite automata with two tapes, the second tape of which is interpreted as programme tape. For fixed automata those classes: of languages are considered, which can be accepted by variation of the programmes. The representation of all regular sets over some alphabet X by a fixed one-way automaton proves to be impossible. This problem has not yet been solved for automata with rewind instructions and two-way automata, which are strongly more powerful than one-way automata.

On a class of automata models of learning machines

Abstract: A class of machines modelled as deterministic Moore automata is proposed. Particular attention is given to investigating their capability of exhibiting learning behaviour assessed by an associated index of performance. This is done by assuming that the automata are operating in a random environment about which they have no a priori knowledge.

On Complete Systems and Finite Automata

Abstract: A production on T* is a rewriting rule σα→σ' for all aϵ T*, where σ, σ' are strings in T* with a' lexicographically earlier than σ. Any finite collection of productions is called a system. This note shows that any system that is consistent, complete, and has the nonprefix property uniquely represents an automaton. This formulation characterizes automata as recognition devices in terms of a set of rewriting rules, similar to the characterizatibn of automata as generating devices by grammars.