Showing papers on "Computability published in 1975"
01 Apr 1975
TL;DR: A framework is presented for the analysis, representation, and evaluation of digital filter structures Based on the notation of linear signal-flow graphs and their equivalent matrix representation, a set of general linear digital network properties are reviewed, including precedence relations computability, Tellegen's theorem, interreciprocity, and network transposition.
Abstract: A framework is presented for the analysis, representation, and evaluation of digital filter structures. Based on the notation of linear signal-flow graphs and their equivalent matrix representation, a set of general linear digital network properties are reviewed, including precedence relations computability, Tellegen's theorem, interreciprocity, and network transposition. These properties are then utilized in developing time and frequency domain analysis techniques and sensitivity analysis techniques. These techniques, in turn, are applied to the comparison of several basic digital filter structures.
207 citations
05 May 1975
TL;DR: A notion of computability on continuous higher types (for all types) is defined and its equivalence to effective operators is shown and shows that the authors' computable operators can model mathematically everything that can be done in an operational semantics.
Abstract: This paper is about mathematical problems in programming language semantics and their influence on recursive function theory. We define a notion of computability on continuous higher types (for all types) and show its equivalence to effective operators. This result shows that our computable operators can model mathematically (i.e. extensionally) everything that can be done in an operational semantics. These new recursion theoretic concepts which are appropriate to semantics also allow us to construct Scott models for the l-calculus which contain all and only computable elements. Depending on the choice of the initial cpo, our general theory yields a theory for either strictly determinate or else arbitrary non-deterministic objects (parallelism). The formal theory is developed in part II of this paper. Part I gives motivation and comparison with related work.
24 citations
TL;DR: It was concluded that learning conditions influenced the integration of cognitive structure in the case of nonsense formulas, while subjects were able to adjust organization of the meaningful formulas.
Abstract: When subjects were required to calculate answers for computable problems and answer questions, an interaction was found corresponding to that obtained by Kieras and Greeno (1975) from judgments of computability. With nonsense formulas, much longer times were required to identify noncomputable problems than to compute answers, with a much smaller difference when formulas consisted of meaningful concepts. The better performance on noncomputable problems and questions with meaningful formulas corroborates an interpretation that those items test the connection of algorithms with general conceptual knowledge. Finally, it was found that for relatively complex problems, solution times and time to judge computability were longer if nonsense formulas were learned in separate sets than if they were learned in a single set; however, no such effect was found with meaningful formulas. It was concluded that learning conditions influenced the integration of cognitive structure in the case of nonsense formulas, while subjects were able to adjust organization of the meaningful formulas.
16 citations
01 Jan 1975
TL;DR: The concept of recognition of fuzzy languages by machines such as Turing machines, linear bounded automata, pushdown automata and finite automata is proposed and it is shown that it is a reasonable extension of the ordinary concept of Recognition of languages by Machines.
Abstract: In this paper, we propose the concept of recognition of fuzzy languages by machines such as Turing machines, linear bounded automata, pushdown automata and finite automata. It is shown that it is a reasonable extension of the ordinary concept of recognition of languages by machines. Basic results are given about the recognition theory of fuzzy languages.
9 citations
01 Sep 1975
TL;DR: An approach to the treatment of solvability and unsolvability notions for mass problems defined on finite sets and a formal scale of solver notions for such mass problems will be proposed.
Abstract: We shall describe an approach to the treatment of solvability and unsolvability notions for mass problems defined on finite sets. A formal scale of solvability notions for such mass problems will be proposed. The general approach follows some concepts of J. yon Neumann [fl], A.N.Kolmogorov [2], A.A.Markov [3], S.V. Jablonskir [4], O.B.Lupanov [5]; it is similar to the concepts of A.I~eyer [6] and A.Ehrenfeucht [7] and continues the concepts described in I~8] and [9] ( in square brackets we shall write the numbers of references and in parentheses the numbers of levels of solvability).
2 citations
TL;DR: In this paper, an idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur.
1 citations