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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TL;DR: It is shown that a large family of modal logics -- including the ones arising from the standard MV and Product algebras -- yields an undecidable consequence relation.
11 citations
TL;DR: This note describes the degree spectra of domains, the set of Turing degrees that compute an isomorphic copy of the structure that is not computably presentable, and discusses similar notions for topological structures.
Abstract: The investigation of computability in topological structures develops in some aspects similar to the investigation of computability in algebraic structures. If a countable algebraic structure is not computably presentable then its ‘‘degree of non-computability’’ is measured by the so called degree spectrum, i.e. the set of Turing degrees that compute an isomorphic copy of the structure. In this note we initiate a discussion of similar notions for topological structures, in particular we describe the degree spectra of domains.
11 citations
TL;DR: An attempt is made to resurrect the pioneering work of Michael Rabin on a class of games that are arithmetically defined and recursion theoretically analysed for effective playability and computational and diophantine complexity.
11 citations
30 Jun 2008
TL;DR: The new version of a tool to assist in teaching formal languages and automata theory can simulate as well push-down automata and Turing machines.
Abstract: In this paper we present the new version of a tool to assist in teaching formal languages and automata theory. In the previous version the tool provided algorithms for regular expressions, finite automata and context free grammars. The new version can simulate as well push-down automata and Turing machines.
11 citations
TL;DR: This work presents a concrete, mathematically precise model of what humans can compute in their heads and provides a method to probe the limits of human computation as well as to design efficient humanly computable mental algorithms for everyday tasks, such as generating passwords and making real-time decisions.
Abstract: What can humans compute in their heads? We are thinking of a variety of cryptographic protocols, games like sudoku, crossword puzzles, speed chess, and so on. For example, can a person compute a function in his or her head so that an eavesdropper with a powerful computer—who sees the responses to random inputs—still cannot infer responses to new inputs? To address such questions, we propose a rigorous model of human computation and associated measures of complexity. We apply the model and measures first and foremost to the problem of 1) humanly computable password generation and then, consider related problems of 2) humanly computable “one-way functions” and 3) humanly computable “pseudorandom generators.” The theory of human computability developed here plays by different rules than standard computability; the polynomial vs. exponential time divide of modern computability theory is irrelevant to human computation. In human computability, the step counts for both humans and computers must be more concrete. As an application and running example, password generation schemas are humanly computable algorithms based on private keys. Humanly computable and/or humanly usable mean, roughly speaking, that any human needing—and capable of using—passwords can if sufficiently motivated generate and memorize a secret key in less than 1 h (including all rehearsals) and can subsequently use schema plus key to transform website names (challenges) into passwords (responses) in less than 1 min. Moreover, the schemas have precisely defined measures of security against all adversaries, human and/or machine.
11 citations