Showing papers on "Computability 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'.

Computability Over Arbitrary Fields

Abstract: In most attempts to make precise the concept of a computable function, or decidable predicate, over a field F, it is considered necessary that the elements of F should be in some sense effectively describable, and hence that F itself should be countable. This is the attitude taken in the study of computable fields (see Rabin1). Our proposed definition of computability over arbitrary fields is based on the Shepherdson - Sturgis2 concept of an unlimited register machine.

R70-21 Time and Tape Complexity of Pushdown Automaton Languages

Abstract: This paper is concerned with the recognition of words which are contained in languages defined by pushdown store machines. Such languages exhibit many of the syntactic properties of algorithmic programming languages. Thus the recognition problem for languages generated by pushdown store machines is related to compilation of programming languages.

Computability Paradigms Based OnDNA Complementarity

Abstract: The paper discusses the fundamental role of the Watson-Crick complementarity in DNA computing. The close relation of the complementarity to the twin-shuffle language guarantees the universal computing power for any model of DNA computing possessing sufficient input and output facilities. Some such models are also briefly discussed.

The emergence of computational arithmetic as a component of the computer science curriculum

Abstract: By computational arithmetic we shall mean the study of those discrete numeric systems suitable for implementation on a digital computer. The structure and limitations of discrete arithmetic, the notions of mixed base and mixed type arithmetic, the incurred “roundoff error” of psuedo-real arithmetic, and the efficiency of realization of arithmetic operations all form integral parts of this discipline. The foundations for this material are drawn from the logician's analysis of computability, the electrical engineer's analysis of boolean networks, the number theorist's analysis of elementary number theory, and the numerical analyst's study of numerical approximation. The cohesive thread uniting these topics is the relevance to computerized discrete computation, and what emerges is a firm discipline for inclusion in the complete Computer Science Curriculum. The central body of this material certainly should be a prerequisite for anyone who must design hardware and/or software to implement the arithmetic called for in a high level language.

A course on the Relationship of Formal Language Theory to Automata

Abstract: This paper describes the second course in a graduate sequence in Computer Science given at the University of Tennessee, Knoxville. The purpose of this sequence is to provide students with a theoretical base in formal language theory for understanding and interpretation of concepts and relationships in programming and automata theory. The explicit purpose of the second course, “The Relationship of Formal Language Theory to Automata”, is to use the structure of grammars, primarily context-free grammars, to examine various aspects of automata theory. These aspects include deterministic and non-deterministic acceptors, processors with pushdown stores, and finite state machines. The first course in the series employs formal language theory as the vehicle for presenting concepts related to the theory of programming languages; this second course employs the same vehicle for presenting aspects of automata theory. The two courses combined achieve a unity whereby important relationships between programming and automata theory as well as applications stemming from these theories can be derived.This course meets for one and a half hours twice a week for ten weeks. Prerequisites for this course include the first course in this sequence, as well as, an intermediate sequence of courses in machine organization and programming languages plus basic courses in numerical analysis, probability and statistics, and at least two years of calculus.