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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: Using this theory, it is shown that engineering design is a computable function and a computational methodology is developed that can be described as a form follows function design paradigm.
Abstract: Computational abstraction of engineering design leads to an elegant theory defining (1) the process of design as an abstract model of computability, the Turing machine; (2) the artifacts of design as enumerated strings from a (possibly multidimensional) grammar; and (3) design specifications or constraints as formal state changes that govern string enumeration. Using this theory, it is shown that engineering design is a computable function. A computational methodology based on the theory is then developed that can be described as a form follows function design paradigm.
12 citations
01 Sep 1997
TL;DR: This work characterize real number complexity classes by purely logical means and mainly finds parallel classes which have not been studied in [10].
Abstract: We study real number complexity classes under a logical point of view. Following the approaches by Blum, Shub, and Smale [3] for computability and by Gradel and Meer [10] for descriptive complexity theory over the reals, we characterize such complexity classes by purely logical means. Among them we mainly find parallel classes which have not been studied in [10].
12 citations
TL;DR: It is shown that computability of the entropy of a subshift does not imply any kind of computation of the language of the subshift, and that any right-computable real number between 0 and 1, whether computable or not, is the entropyof some subshift with even polynomial time decidable language.
Abstract: We consider subshifts of the full shift of all binary bi-infinite sequences. On the one hand, the topological entropy of any subshift with computably co-enumerable language is a right-computable real number between 0 and 1. We show that, on the other hand, any right-computable real number between 0 and 1, whether computable or not, is the entropy of some subshift with even polynomial time decidable language. In addition, we show that computability of the entropy of a subshift does not imply any kind of computability of the language of the subshift
12 citations
01 Jan 1989
TL;DR: A fully-described program in Pascal has been included and serves a two-fold purpose: it exposes concrete practical solutions, which encourages the reader to try other strategies on his (her) own, and allows to check the correctness of different theoretic concepts emerging from the Method of Maximal Adjacencies.
Abstract: One of the central problems in the physical realization of sequential machines is the selection of binary codes to represent the internal states of the machine. The Method of Maximal Adjacencies can be viewed as an approach to the state assignment problem. This research report concentrates on simple, practical strategies to implement that method. A fully-described program in Pascal has been included and serves a two-fold purpose: (1) it exposes concrete practical solutions, which encourages the reader to try other strategies on his (her) own; (2) it has been conceived from a general standpoint that allows to check the correctness of different theoretic concepts emerging from the Method of Maximal Adjacencies. A set of industrial sequential machines has been chosen to test the program. Results from other existing methods have been also reported.
12 citations