Axiomatic Tools versus Constructive approach to Unconventional Algorithms

TL;DR

This paper examines the philosophical and methodological implications of unconventional algorithms, highlighting how new models have expanded the algorithmic universe and necessitated advanced axiomatic tools for their analysis.

Contribution

It provides an analysis of the axiomatic and constructive approaches to unconventional algorithms, emphasizing the need for new tools to understand their increased complexity.

Findings

New models of algorithms expand the algorithmic universe.

Axiomatic tools are essential for analyzing complex unconventional algorithms.

The approach enhances understanding of algorithmic flexibility and creativity.

Abstract

In this paper, we analyze axiomatic issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms changed the algorithmic universe, making it open and allowing increased flexibility and creativity. However, the greater power of new types of algorithms also brought the greater complexity of the algorithmic universe, demanding new tools for its study. That is why we analyze new powerful tools brought forth by the axiomatic theory of algorithms, automata and computation.