3 research outputs found
Finite Computational Structures and Implementations
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.Comment: 12 pages, 3 figures, will be presented at CANDAR'16 and final version
published by IEEE Computer Societ
The Algebraic View of Computation
We argue that computation is an abstract algebraic concept, and a computer is
a result of a morphism (a structure preserving map) from a finite universal
semigroup.Comment: 13 pages, final version will be published elsewher