Showing papers on "ω-automaton published in 1966"

Communication with automata

Abstract: The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem. The argument proceeds as follows: 1. We assume the following postulates: a) there exists an upper bound on the speed of signals; b) there exists an upper bound on the density with which information can be stored. 2. Automata of fixed, finite size can recognize, at best, only iteratively defined classes of input sequences. (See Kleene (11) and Copi, Elgot, and Wright (8).) 3. Recursively defined classes of input sequences that cannot be defined iteratively can be recognized only by automata of unbounded size. 4. In order for an automaton to solve a (soluble) recursive problem, the possibility must be granted that it can be extended unboundedly in whatever way might be required. 5. Automata (as actual hardware) formulated in accordance with automata theory will, after a finite number of extensions, conflict with at least one of the postulates named above. Suitable conceptual structures for an exact theory of communication are then discussed, and a theory of communication proposed. All of the really useful results of automata theory may be expressed by means of these new concepts. Moreover, the results retain their usefulness and the new nrocedure has definite advantages over the older ones. The proposed representation differs from each of the presently known theories concerning information on at least one of the following essential points: 1. The existence of a metric is assumed for either space nor time nor for other physical magnitudes. 2. Time is introduced as a strictly local relation between states. 3. The objects of the theory are discrete, and they are combined and produced only by means of strictly finite techniques. The following conclusions drawn from the results of this work may be cited as of some practical interest: 1. The tolerance requirements for the response characteristics of computer components can be substantially weakened if the computer is suitably structured. 2. It is possible to design computers structurally in such a way that they are asynchronous, all parts operating in parallel, and can be extended arbitrarily without interrupting their computation. 3. For complicated organizational processes of any given sort the theory yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata. Diese Arbeit befasst sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, moglichst viele Erscheinungen bei der Informationsubertragung und Informationswandlung in einheitlicher und exakter Weise zu beschreiben.

Two Complete Axiom Systems for the Algebra of Regular Events

Abstract: The theory of finite automata is closely linked with the theory of Kleene's regular expressions. In this paper, two formal systems for the algebraic transformation of regular expressions are developed. Both systems are consistent and complete; i.e., the set of equations derivable within the system equals the set of equations between two regular expressions denoting the same event. One of the systems is based upon the uniqueness of the solution of certain regular expression equations, whereas some facts concerning the representation theory of regular events are used in connection with the other.

Simple self-reproducing universal automata

Abstract: von Neumann and Thatcher have shown that one may construct self-reproducing universal arrays using as basic cells finite automata with only 29 states. The simplicity of the components necessitates complex programming. We present a self-reproducing universal array with simple programming. This is made possible by using as basic unit a finite automaton which can execute an internal program of up to 20 instructions.

About Some Properties of Definite, Reverse-Definite and Related Automata

Abstract: For reduced finite Moore automata corresponding to regular expressions which are finite sums of expressions of the form E+H?*G (E, H, G are finite events and ? is the set of inputs) it is shown that an arbitrary change of the initial state or of the set of final states results in an automaton belonging to the same class. The transition graphs corresponding to the single inputs in definite and reverse-definite automata are investigated.

COMMUNICATION WITH AUTOMATA: Volume 1 Supplement 1

Abstract: : The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem. The argument proceeds as follows: (1) The following postulates are assumed: (a) there exists an upper bound on the speed of signals; (b) there exists an upper bound on the density with which information can be stored. (2) Automata of fixed, finite size can recognize, at best, only iteratively defined classes of input sequences. (3) Recursively defined classes of input sequences that cannot be defined iteratively can be recognized only by automata of unbounded size. (4) in order for an automaton to solve a (soluble) recursive problem, the possibility must be granted that it can be extended unboundedly in whatever way might be required. (5) Automata (as actual hardware) formulated in accordance with automata theory will, after a finite number of extensions, conflict with at least one of the postulates. Suitable conceptual structures for an exact theory of communication are then discussed, and a theory of communication proposed.

Group-Type Automata

Abstract: The purpose is to investigate the input structure of automata which have a group-like character. The class of perfect automata investigated by Fleck in [2] and Weeg in [6] is a proper subclass of those considered here.

Block-stochastic matrices and associated finite-state languages

Abstract: Finite automata are considered whose transition matrix is blockstochastic. The block-stochastic structure defines an equivalence relation among states of the automata. The implications of this relation are investigated, especially with respect to the languages accepted in the states of the automata.

On the Class of Predicates Decidable by Two-Way Multitape Finite Automata

Abstract: The problem of deciding predicates concerned with m-tuples of words by means of 2-way multitape finite automata is considered. In general, more than m tapes are used to decide a predicate concerned with m-tuples of words. In such a way, a necessary and sufficient condition for a predicate to be decidable by a 2-way multitape finite automaton is obtained. The relation between the ability of Turing machines and that of 2-way multitape finite automata is also discussed.

Generalized decomposition of incomplete finite automata

Abstract: The problem of decomposing a finite automaton has been investigated by many authors [7,8,9,16] However, their results were based on the question of decomposing an automaton into series and parallel connections of automata The present work is an extension to the problem of generalized decomposition where two-way interconnections between automata are permitted Our decomposition does not presuppose the logical design of the circuit of an automaton With the new technology, the problem of economical realization no longer lies in the actual complexity of the logical design in each building block Aside from a given upper limit, the complexity is not reflected in the cost Subject to the restraint of the given limit on each block, the main object is to minimize the number of interconnections between blocks of a generalized decomposition of an automaton

Synthesis of automata by decomposition techniques.

Abstract: : The major effort under this research program was devoted to parallel decompositions of single-input automata (autonomous sequential machines) without and with state-splitting. First, decompositions into two smaller automata subject to suitable optimality criteria were considered and computational decomposition techniques were established. Next, indecomposable single-input automata (modules) were characterized and methods were derived for the realization of any specified single-input automaton as parallel composition of such modules. Some results concerning cascade decompositions of single-input automata are also given. The other part of this research program was devoted to establishing a mathematically precise, basic theory for generalized cascade decompositions of partially specified multi-input semi-automata (output-free sequential machines). Earlier work by Yoeli was unified with recent work on complete automata by Zeiger. The concept of homomorphic relation plays an important role in this connection. (Author)