Formalizing the notions of non-interactive and interactive algorithms

C. A. Middelburg

doi:10.47743/sacs.2025.2.211

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arXiv · 2405.19037

Formalizing the notions of non-interactive and interactive algorithms

C. A. Middelburg

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Abstract

An earlier paper gives an account of a quest for a satisfactory formalization of the classical informal notion of an algorithm. That notion only covers algorithms that are deterministic and non-interactive. In this paper, an attempt is made to generalize the results of that quest first to a notion of an algorithm that covers both deterministic and non-deterministic algorithms that are non-interactive and then further to a notion of an algorithm that covers both deterministic and non-deterministic algorithms that are interactive. The notions of an non-interactive proto-algorithm and an interactive proto-algorithm are introduced. Non-interactive algorithms and interactive algorithms are expected to be equivalence classes of non-interactive proto-algorithms and interactive proto-algorithms, respectively, under an appropriate equivalence relation. On both non-interactive proto-algorithms and interactive proto-algorithms, three equivalence relations are defined. Two of them are deemed to be bounds for an appropriate equivalence relation and the third is likely an appropriate one.

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C. A. Middelburg. 2024-05-29. Formalizing the notions of non-interactive and interactive algorithms. https://doi.org/10.47743/sacs.2025.2.211

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