Abstract: The existing, intuitive computation models, that is the virtual machines of Turing, Post, Kolmogorov, Schönhage, Aho-Ullman-Hopcroft? as well as the algorithms of Markov and Krinitski, and the recursive functions, all lack precise, mathematical formulation. Consequently, algebra of algorithms is defined using the axiomatic method. The algebra is based on the operations of sequencing, elimination, paralleling and reversing as well as cyclic sequencing, cyclic elimination and cyclic paralleling, all of them performed on the so-called uniterms. A useful extension is offered in terms of additional cycle elimination axiomats. A simple example illustrates the usefulness of the algebra of algorithms.

Keywords: Computation models, algorithms, algebra of algorithms, operations.

ACM Classification Keywords: I.0 General Literature

Link:

THE EXTENDED ALGEBRA OF ALGORITHMS WITH ADDITIONAL CYCLE ELIMINATION AXIOMATS

Volodymyr Ovsyak, Aleksandr Ovsyak

http://foibg.com/ibs_isc/ibs-24/ibs-24-p03.pdf