Topic

# Computability

About: Computability is a(n) research topic. Over the lifetime, 2829 publication(s) have been published within this topic receiving 85162 citation(s).

##### Papers published on a yearly basis

##### Papers

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01 Jan 1979

TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

13,555 citations

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TL;DR: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.

3,665 citations

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Romanian Academy

^{1}TL;DR: It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.

Abstract: We introduce a new computability model, of a distributed parallel type, based on the notion of a membrane structure. Such a structure consists of several cell-like membranes, recurrently placed inside a unique “skin” membrane. A plane representation is a Venn diagram without intersected sets and with a unique superset. In the regions delimited by the membranes there are placed objects. These objects are assumed to evolve: each object can be transformed in other objects, can pass through a membrane, or can dissolve the membrane in which it is placed. A priority relation between evolution rules can be considered. The evolution is done in parallel for all objects able to evolve. In this way, we obtain a computing device (we call it a P system): start with a certain number of objects in a certain membrane and let the system evolve; if it will halt (no object can further evolve), then the computation is finished, with the result given as the number of objects in a specified membrane. If the development of the system goes forever, then the computation fails to have an output. We prove that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice. In fact, we do not need cooperating rules, but we only use catalysts, specified objects which are present in the rules but are not modified by the rule application. One catalyst suffices. A variant is also considered, with the objects being strings over a given alphabet. The evolution rules are now based on string transformations. We investigate the case when either the rewriting operation from Chomsky grammars (with respect to context-free productions) or the splicing operation from H systems investigated in the DNA computing is used. In both cases, characterizations of recursively enumerable languages are obtained by very simple P systems: with three membranes in the rewriting case and four in the splicing case. Several open problems and directions for further research are formulated

2,182 citations

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01 Mar 1974

TL;DR: This book attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in formal languages and automata, written by Professor Ian Chiswell.

Abstract: The 80 revised papers presented together with two keynote contributions and four invited papers were carefully reviewed and sele... The study of formal languages and automata has proved to be a source of much interest and discussion amongst mathematicians in recent times. This book, written by Professor Ian Chiswell, attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest i...

2,011 citations

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01 Jun 1989

TL;DR: The neural computing theory and practice book will be the best reason to choose, especially for the students, teachers, doctors, businessman, and other professions who are fond of reading.

Abstract: In what case do you like reading so much? What about the type of the neural computing theory and practice book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining books become so popular this day. Besides, the scientific books will also be the best reason to choose, especially for the students, teachers, doctors, businessman, and other professions who are fond of reading.

1,834 citations