Topic
Computability
About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.
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01 Jan 1990
15 citations
TL;DR: The key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic are discussed.
Abstract: We give a survey of the study of nonstandard models in recursion theory and reverse mathematics. We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic. Particular attention is given to principles related to Ramsey’s Theorem for Pairs.
15 citations
Journal Article•
TL;DR: It is shown that this result is preserved when considering rewriting modulo a set of equations if the equivalence classes generated by these equations are finite, the equations are linear and satisfy general syntactic conditions also based on the notion of computability closure.
Abstract: We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous work, we defined general syntactic conditions based on the notion of computability closure for ensuring the termination of the combination of rewriting and β-reduction. Here, we show that this result is preserved when considering rewriting modulo a set of equations if the equivalence classes generated by these equations are finite, the equations are linear and satisfy general syntactic conditions also based on the notion of computability closure. This includes equations like associativity and commutativity and provides an original treatment of termination modulo equations.
15 citations
14 Jun 2015
TL;DR: This approach, based on examining the underlying common randomness, provides a new proof of the characterization of a securely computable function by deterministic protocols, and yields a characterization of the minimum communication needed for secure computability.
Abstract: We revisit A.C. Yao's classic problem of secure function computation by interactive communication, in an information theoretic setting. Our approach, based on examining the underlying common randomness, provides a new proof of the characterization of a securely computable function by deterministic protocols. This approach also yields a characterization of the minimum communication needed for secure computability.
15 citations
14 Jan 1974
TL;DR: Motivated by practical implementation-methods for recursive program-schemata, presetting techniques for push-down automata are defined and study and the languages of preset pda's are characterized in terms of types of iterated substitution languages.
Abstract: Motivated by practical implementation-methods for recursive program-schemata we will define and study presetting techniques for push-down automata. The main results will characterize the languages of preset pda's in terms of types of iterated substitution languages. In particular when conditions of "locally finiteness" and of "finite returning" are imposed we get a feasible machine-model for a class of developmental languages. The accepted family extends to the smallest AFL enclosing it when we drop the condition of locally finiteness. At the same time this family will be the smallest such full AFL. If all conditions are removed, present pda's exactly represent the family of iterated regular substitution languages, a sub-family of the indexed languages. Deterministic preset pda's are also studied, and the language-family they define is shown to be closed under complementation, generalizing a classical result.
15 citations