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When are Two Algorithms the Same?

  • Andreas Blass (a1), Nachum Dershowitz (a2) and Yuri Gurevich (a3)

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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[3] Andreas Blass and Yuri Gurevich , Ordinary interactive small-step algorithms, ACM Transactions on Computational Logic, Part I, vol. 7 (2006), pp. 363419, Part II, vol. 8 (2007), article 15, and Part III, vol. 8 (2007), article 16.

[9] Jean-Yves Girard , Linear logic, Theoretical Computer Science, vol. 50 (1987), pp. 1101.

[11] Yuri Gurevich , Sequential abstract state machines capture sequential algorithms, ACM Transactions on Computational Logic, vol. 1 (2000), pp. 77.

[14] Joachim Lambek , Deductive systems and categories. I. Syntactic calculus and residuated categories, Mathematical Systems Theory, vol. 2 (1968), pp. 287.

[19] Stephen Simpson , Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, 1999.

[20] Alfred Tarski , Undecidable theories, North-Holland, 1953, with the collaboration of Andrzej Mostowski and Raphael Robinson.

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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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