Showing papers on "ω-automaton published in 1970"

Switching and automata theory.

Abstract: : The research under the grant consisted of the following projects: (1) Extensive development of the theory of linear sequential circuits; (2) Solution of various problems in the theory of finite-state automata, including the counting of such automata, error correction capability, realization by input-output relations, periodicity properties and equivalence problems; (3) Solution of problems in the theory of stochastic automata and time-varying automata; (4) Research in formal languages, including context-free languages and multi-tape, multi-head pushdown automata; and (5) Solution of various operations-research type problems, such as optimization algorithms for finite, directed, weighted graphs, and the 'change-making problem'.

Cellular automata and formal languages

Abstract: A set of equivalences is established among cellular automata, iterative acceptors, and linear-bounded automata However, cellular automata are shown to be inherently faster than iterative acceptors Many positive results are presented to indicate that the context-free languages can, perhaps, be accepted in time n and space n by cellular automata

The Garden-of-Eden theorem for finite configurations

Abstract: In [l] Moore showed that the existence of mutually erasable configurations in a two-dimensional tessellation space is sufficient for the existence of Garden-of-Eden configurations. In [2 ] Myhill showed that the existence of mutually indistinguishable configurations is both necessary and sufficient for the existence of Garden-of-Eden configurations. After redefining the basic concepts with some minor changes in terminology, and after restating the main results from [l] and [2], we shall establish the equivalence between the existence of mutually erasable configurations and the existence of mutually indistinguishable configurations. This implies that the converse of Moore's result is true as well. We then show that by limiting the universe to the set of all finite configurations of the tessellation array, both of the above conditions remain sufficient, but neither is then necessary. Finally, we establish a necessary and sufficient condition for the existence of Garden-of-Eden configurations when only finite configurations are considered. I. The tessellation structure and the Garden-of-Eden theorems. The tessellation array, which was first used by Von Neumann [3] in obtaining his results on machine self-reproduction, can be visualized as an infinite two-dimensional Euclidean space divided into square cells, in the fashion of a checkerboard, where each cell can hold any symbol from a finite set A. We use the set Z2 of ordered pairs of integers to name the cells in the tessellation array. An array configuration, i.e., a symbol placed in each cell, is formally a mapping c'.Z2—>A. The restriction of an array configuration c to a subset 5 of Z2 will be denoted by (c)sWe speak of this as the configuration of S in array configuration c. Each cell will behave like a deterministic and synchronous finite-state machine, and the symbol in cell (i, j) at time / will depend on the symbol in cell (i, j) at time t — 1 as well as the symbols in certain neighboring cells at time t — 1. In this paper, as in [l] and [2], we fix the neighbors of any cell to be those cells (including the cell itself) which have each of their coordinates differing by at most 1 from the coordinate of the given cell. Figure 1 shows the neighbors of cell (i, j). Received by the editors September 2, 1969 and, in revised form, November 3, 1969. A MS subject classifications. Primary 0288, 0280, 9440.

Finite state automation: definition of data communication line control procedures

Abstract: The notions of finite state automata, state transition graphs and tables and the set of regular languages being accepted (generated) by such automata are well known. But for some reason these notions have not been rigorously applied in the definition of data communication line control procedures. It is the objective of this paper to do so and to show the naturalness of this approach. We claim that we thereby arrive at a complete, precise and unambiguous definition. Others have attempted this before us. They have, however, not used the descriptional tool of finite state automata. Any one or all of these references thus form the basis on which we will compete and we shall use essentially the line control procedures which these documents set out to define.

Linked probabilistic finite automata: A model for the temporal interaction of speakers

Abstract: A speaker is modeled as a probabilistic finite automaton with four internal states and input and output alphabets of 0 (silence) and 1 (sound). With identically zero input the model generates a two-state Markov chain that accounts for the on-off pattern of monologue. Two such automata, possessing the same type of decision rules, are coupled so that the output of each is input to the other. The six-state deep structure of the linked system, projected as a four-state observable sequence, can be accounted for using only three parameters per speaker. Consequences of the model yield testable predictions about the relations between monologue, dialogue, and speech under delayed auditory feedback.

On the relationship between finite automata, finite monoids, and prefix codes.

Abstract: It is the aim of the present study to establish links between the structure of a given (finite) prefixcode and that of its syntactic monoid, using automata theory as a tool.

On asynchronous stochastic automata

Abstract: The paper deals with generalized stochastic automata (probabilistic sequential machines) which are able to print not only a single output but an output tape of arbitrary finite length each unit of time. Section 1 contains the basic definitions and some observations concerning the basic probabilities which are associated with each stochastic automaton. In section 2 the equivalence of situations and of automata is investigated. The principal result is the decidability of equivalence of finite situations of finite automata. Section 3, the main portion of the paper, is devoted to an investigation of the input-output relations, i.e., of the externally observable behavior, of stochastic automata. The existence of a so-called state family is shown to be a criterion for the generability of a stochastic operator within a stochastic automaton. The nonuniqueness of state families leads to a consideration of separability of stochastic operators, a property being, for generable stochastic operators, necessary and sufficient for the uniqueness of a state family. This property as well as a somewhat weaker property is characterized then. Some open problems are pointed out.

Two-state two-symbol probabilistic automata

Abstract: In this paper, we discuss the algebraic treatments of probabilistic automata with two states. We derive the result that the matrix product corresponding to a given input tape can be decomposed into the sum of a finite number of fundamental matrices which are determined by the matrices corresponding to the input symbols. We introduced the new concept of probabilistic automata completely isolated by the L -th approximation . With respect to these automata, all tapes of length greater than or equal to L + 1 can be classified into 2{su L +1} sets by means of their ( L + 1)-suffixes. By using this concept, we demonstrate that a two-input symbol actual automaton with two states can realize any definite event.

Minimal linear realizations of autonomous automata

Abstract: In the theory of finite automata minimal linear realizations of automata are of great interest. One can show that in the case of autonomous automata without output function it is sufficient to find minimal linear realizations of special types of automata, namely of permutations and of trees. Deriving this result we furthermore get the uniqueness of the minimal linear realization of a tree.

The theory of interacting local automata

Abstract: Local automata are defined as labeled monadic algebras that interact and accept or reject each other. The relationship between deterministic and non-deterministic local automata is established. Then the algebraic closure properties of acceptable classes of structures in terms of homomorphisms, direct products, and reduced products are studied. It is shown that multiinput local automata accept precisely those classes of structures that are models of sentences in first-order monadic logic without equality. Equality can be introduced with an extension of the theory. A finite local automaton may, in general, accept the models of an infinite sentence that is not equivalent to any finite sentence.

An Improved Upper Bound for the Finite Delay of Graphs

Abstract: The notion of graphs solvable with finite delay appears in [1] and [4]. In this note the upper bound on finite delay for a graph with N nodes is reduced to the order of 2N2using techniques from finite automata theory.

A method of coding the states of finite automata from the point of view of minimizing equipment expenditures

Abstract: : A method is proposed for coding the states of finite automata to minimize the equipment necessary for realization. The problem arises in the synthesis of control automata that must possess means for decoding each state during formation of the output control signals. The method consists in representing the automaton as a composition of the simplest partial automata.

On the number of automorphisms of a singly generated automaton

Abstract: searched only if we replace the \"fixed constmlt\" by a number congruent to-Q/v2. However, even if this is done, there is still the problem that when Q ~-0, only one table location is examined! To correct these problems, replace steps (3) and (4) of Bell's algorithm with: (3) Initialize A with C, where C is defined below. (4) Increment A by 2Q. For this algorithm, we have a = Q + C, b = Q. We must then choose C so that C ~-QifQ ¢ 0andC ¢-Qif Q ~-0. The algorithm will then search (p + 1)/2 locations if Q ~ 0, and will search all p locations if Q-= 0. The trouble with this algorithm is that it requires testing for Q ~ 0, which means performing an extra division. A seemingly possible way out is to observe that if (p-a)/vb-j, b ¢ 0, then the algorithm searchesj fewer locations before it starts reexamining locations. We can then try to choose C so that we get j to be small, thereby examining nearly half the table before repeating. However, this requires that we make C ~-(j + 1)Q. There does not appear to be any simple algorithm for choosing a C satisfying this congruence for a small j when Q fi 0, and choosing C ¢-Q when Q ~ 0. ~ It seems that the division is necessary. The corrected version of Bell's algorithm still contains a gross inefficiency. For Q ~ 0, it decided that the search is a failure after p tries, instead of the necessary (p q-1)/2 tries. This is easily corrected by changing the criterion for failure. In summary, Bell's algorithm requires a correction which adds an extra division to the initialization procedure. This must be considered in evaluating its efficiency. Bell's table comparing the efficiency of his method with that of Maurer's indicates that this extra initialization cost is justified only if checking a single entry is a relatively time consuming operation.

Direct and subdirect product structure theorems for non-deterministic automata

Abstract: A complete non-deterministic automaton may be viewed as a relational system with unary and binary relations. These relations must satisfy certain closure properties. On the basis of these properties, recent results concerning the representation of general relational systems as direct and subdirect products are specialized to more precise results for non-deterministic automata. For example, we prove that the representations of a non-deterministic automaton as a direct product correspond in a one-to-one way to certain families ofideals of the automaton. The ideal of an automaton are seen to play an essential role in describing its structure, and a number of the properties of ideals are delineated.