When are two algorithms the same?
Andreas Blass (University of Michigan), Nachum Dershowitz (Tel Aviv, University), and Yuri Gurevich (Microsoft Research)
TL;DR
This paper investigates the formal relationship between algorithms and programs, arguing that algorithms cannot be precisely defined as equivalence classes of programs under any suitable relation.
Contribution
It challenges the common assumption that algorithms can be formalized as equivalence classes of programs, providing a philosophical and formal argument against this idea.
Findings
No suitable equivalence relation exists for formalizing algorithms as classes of programs.
Algorithms are inherently more abstract than their implementations.
The paper clarifies the conceptual distinction between algorithms and programs.
Abstract
People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · semigroups and automata theory