International Journal of Networking and Computing
Online ISSN : 2185-2847
Print ISSN : 2185-2839
ISSN-L : 2185-2839
Special Issue on the Fourth International Symposium on Computing and Networking
Finite Computational Structures and Implementations: Semigroups and Morphic Relations
Attila Egri-Nagy
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2017 Volume 7 Issue 2 Pages 318-335

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Abstract

What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only partial answers to these questions. To make these problems more precise and easier to tackle, we describe an abstract algebraic definition of classical computation by generalizing traditional models to semigroups. This way implementations are morphic relations between semigroups. The mathematical abstraction also allows the investigation of different computing paradigms (e.g. cellular automata, reversible computing) in the same framework. While semigroup theory helps in clarifying foundational issues about computation, at the same time it has several open problems that require extensive computational efforts. This mutually beneficial relationship is the central tenet of the described research.

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