Showing papers on "ω-automaton published in 1967"

Automata on a 2-dimensional tape

Abstract: This paper explains our approach to the problem of pattern recognition by serial computer. The rudimentary theory of vision presented here lies within the framework of automata theory. Our goal is to classify the types of patterns that can be recognized by an automaton that scans a finite 2-dimensional tape. For example, we would like to know if an automaton can decide whether or not a given pattern on a tape forms a connected region. Although we have solved a number of problems, we have failed to solve this connectedness problem. This paper merely begins to describe the action of automata in higher dimensions. Our goal now is to generalize the theory presented here and make it applicable to a wide variety of pattern-recognizing machines.

Codes, automata, and continuous systems: Explicit interconnections

Abstract: Close relationships are established between convolutional codes and zero-state automata and between cyclic codes and zero-input automata. Furthermore, techniques of automata theory and continuous system theory are used to elaborate on the coding problem; and approaches from coding and automata are used to establish and interpret typical structural conditions in continuous systems. The investigation incorporates basic coding concepts into the currently emerging common basis for automata and continuous systems, and it gives explicit examples of the resulting benefits accruing to each of these areas from the others.

Introduction to the Theory of Finite Automata

Abstract: In what case do you like reading so much? What about the type of the introduction to the theory of finite automata book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining books become so popular this day. Besides, the scientific books will also be the best reason to choose, especially for the students, teachers, doctors, businessman, and other professions who are fond of reading.

Enumeration of finite automata

Abstract: Harary ( 1960, 1964), in a survey of 27 unsolved problems in graphical enumeration, asked for the number of different finite automata. Recently, Harrison (1965) solved this problem, but without considering automata with initial and final states. With the aid of the Power Group Enumeration Theorem (Harary and Palmer, 1965, 1966) the entire problem can be handled routinely. The method involves a confrontation of several different operations on permutation groups. To set the stage, we enumerate ordered pairs of functions with respect to the product of two power groups. Finite automata are then concisely defined as certain ordered pah's of functions. We review the enumeration of automata in the natural setting of the power group, and then extend this result to enumerate automata with initial and terminal states.

An approach to a unified theory of automata

Abstract: An automaton called the balloon automaton is defined The balloon automaton comes in four varieties, depending on whether the device is deterministic or nondeterministic, and whether the input head can move in one or two directions Subsets of the balloon automata of each variety, called closed classes are defined Almost all the known types of automata are equivalent to some closed class of balloon automata Properties of closed classes are given For example, whatever the variety, the languages accepted by a closed class are closed under intersection with a regular set For a given organization of storage, closed classes of the four varieties can be defined These four classes are said to form a family A class may be recursive or not, and the emptiness problem may be solvable or unsolvable Some surprising relationships exist between the recursiveness and solvability of emptiness for the classes in a family

Yet another proof of the cascade decomposition theorem for finite automata

Abstract: We give here a short proof that each finite automaton can be built as a cascade of permutation automata and identity-reset automata.

Adaptation of stochastic automata in nonstationary environments

Abstract: This paper considers the effect of environmental nonstationarities on the performance of a stochastic automaton when it is used in the synthesis of an adaptive controller. The stochastic automaton considered has a variable structure in that its state probabilities are continuously altered according to a reinforcement scheme in response to penalties received from the environment. The automaton adapts by reducing the average penalty. Periodic perturbations of penalty strengths are used as "test signals" to derive analytic expressions describing the "tracking" behavior of the automaton operating under a linear reinforcement scheme. The pertinent parameters governing the adaptive behavior are discussed in detail. Digital simulation studies are presented for 2-state and 10-state cases. The results agree with the theoretical analysis.

Programming Language for Automata

Abstract: The techniques of automatic programming are useful for constructive proofs in automata theory. A formal definition of an elementary programming language for a stack automaton is given, and it is shown how this may be readily adapted to other classes of automata. The second part of this paper shows how this programming language can be applied to automata theory, as we prove there are non-context-sensitive languages accepted by a stack automaton.

Real time counter machines

Abstract: An automaton called the balloon automaton is defined The balloon automaton comes in four varieties, depending on whether the device is deterministic or nondeterministic, and whether the input head can move in one or two directions Subsets of the balloon automata of each variety, called closed classes are defined Almost all the known types of automata are equivalent to some closed class of balloon automata Properties of closed classes are given For example, whatever the variety, the languages accepted by a closed class are closed under intersection with a regular set For a given organization of storage, closed classes of the four varieties can be defined These four classes are said to form a family A class may be recursive or not, and the emptiness problem may be solvable or unsolvable Some surprising relationships exist between the recursiveness and solvability of emptiness for the classes in a family

Computation times for finite groups, semigroups and automata

Abstract: In this paper two closely related problems in automata theory are considered: 1) What is the time required for a network of elements, each with a limited number of inputs, to compute a finite function? 2) What is the time required for a finite automaton, realized as such a network, to compute its output function? Winograd has considered the first problem, especially for addition and group multiplication [1] and numerical multiplication [2]. By laying bare the methodology implicit in his work, we form a basis upon which we can erect a thoroughgoing analysis of multiplication in groups and semigroups and also can analyze computation of various finite functions. This paper presents the beginning of such an analysis.

On the decomposability of monadic algebras and automata

Abstract: The structure connections between the endomorphisms, automorphisms, and all congruence relations of an arbitrary, not necessarily finite or strongly connected automaton are investigated It is shown how the symmetries of an automaton carry over to symmetries of the lattice of congruence relations and to symmetries of quotient automata A Galois connection is established between the endomorphisms and the congruence relations of an automaton

A parallel-acting iterative automaton

Abstract: deterministic automata are defined in an attempt to capture the essential features of an iterative one-dimensional array of finite-state machines operating under the direction of a central control where at discrete time steps each machine in the chain is receiving the same instruction as each of the other machines Each machine in the array is also capable of direct communication only with immediately neighboring machines Some general theory is developed, and the sets of strings definable by these automata are described

On endomorphisms and congruences of automata

Abstract: The structure connections between the endomorphisms, automorphisms, and all congruence relations of an arbitrary, not necessarily finite or strongly connected automaton are investigated It is shown how the symmetries of an automaton carry over to symmetries of the lattice of congruence relations and to symmetries of quotient automata A Galois connection is established between the endomorphisms and the congruence relations of an automaton

On the complexity of undecidable problems in automata theory

Abstract: This paper describes some general results about hierarchies of undecidable problems in automata theory, and studies how properties of sets accepted by automata change from decidable to undecidable problems as the memory capacity of the automaton is increased

On Multiple Finite Automata

Abstract: The k-multiple automata introduced in this paper are devices for the recognition (or generation) of languages rather than transducers devices providing sequential mappings of the input sequences into the output ones. The new and most important and powerful step in the recognition procedure provided by a k-multiple automaton is that the considered string is divided into k parts of the same length. Further these parts are recognized “simultaneously” by k simple, i.e. ordinary automata, which are controlled by a single and common transition function. This is an explanation why the multiple automata can be much more powerful than the simple ones.