Finite Computational Structures and Implementations
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. In order to make these problems more precise, we describe an abstract algebraic definition of classical computation, generalizing traditional models to semigroups. The mathematical abstraction also allows the investigation of different computing paradigms (e.g. cellular automata, reversible computing) in the same framework. Here we summarize the main questions and recent results of the research of finite computation.
 Publication:

arXiv eprints
 Pub Date:
 October 2016
 arXiv:
 arXiv:1610.05849
 Bibcode:
 2016arXiv161005849E
 Keywords:

 Computer Science  Other Computer Science;
 Mathematics  Group Theory;
 20M20;
 20M35;
 68Q70;
 68Q05;
 F.1.1;
 F.4.0
 EPrint:
 12 pages, 3 figures, will be presented at CANDAR'16 and final version published by IEEE Computer Society