When are two algorithms the same?

Bulletin of Symbolic Logic

Volumn 15, Issue 2, 2009, Pages 145-168

  Blass, Andreas ^a   Dershowitz, Nachum ^b   Gurevich, Yuri ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c MICROSOFT RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649961006     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2178/bsl/1243948484     Document Type: Article

References (23)

1. ALFRED AHO, JOHN HOPCROFT, and JEFFREY ULLMAN, The design and analysis of computer algorithms, Addison-Wesley, 1974.
2. ANDREAS BLASS and YURI GUREVICH, Algorthms: A quest for absoute definitions, Bulletin of the European Association for Theoretical Computer Science, vol. 81 (2003), pp. 195-225.
3. -, Ordinary interactive small-step algorithms, ACM Transactions on Computational Logic, Part I, vol. 7 (2006), pp. 363-419, Part II, vol. 8 (2007), article 15, and Part III, vol. 8 (2007), article 16.
4. NICOLAS BOURBAKI, Eléments de mathématique XVII, première partie: Les structures fondamentales de l'analyse, Livre I. Théorie des ensembles, Hermann & Cie, 1954, English translation Theory of sets, Hermann and Addison-Wesley, 1968, reprinted by Springer-Verlag (2004).
5. SAMUEL BUSS, ALEXANDER KECHRIS, ANAND PILLAY, and RICHARD SHORE, The prospects for mathematical logic in the twenty-first century, this Bulletin, vol. 7 (2001), pp. 169-196.
6. NICOLAAS DE BRUIJN, Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem, Koninklijke Nederlandse Akademie van Wetenschappen Proc. Ser. A, vol. 75 = Indagationes Mathematicae, vol. 34 (1972), pp. 381-392.
7. NACHUM DERSHOWITZ and YURI GUREVICH, A natural axiomatization of computability and proof of Church's thesis, this BULLETIN, vol. 14 (2008), pp. 299-350.
8. HARVEY FRIEDMAN, Some systems of second-order arithmetic and their use, Proceedings of the International Congress of Mathematicians, Vancouver 1974, vol. I, 1975, pp. 235-242.
9. JEAN-YVES GIRARD, Linear logic, Theoretical Computer Science, vol. 50 (1987), pp. 1-101.
10. YURI GUREVICH, Evolving algebras: Lipari guide, Specification and validation methods (E. Börger, editor), Oxford University Press, 1995, pp. 9-36.
11. -, Sequential abstract state machines capture sequential algorithms, ACM Transactions on Computational Logic, vol. 1 (2000), pp. 77-111.
12. DAVID JOYCE, Euclid's elements, web page at http://alephO.claxku.edu/~djoyce/java/elements/elements.html (viewed on January 27, 2008.).
13. DONALD E. KNUTH, Sorting and searching, The art of computer programming, vol. 3, Addison-Wesley, 1973.
14. JOACHIM LAMBEK, Deductive systems and categories. I. Syntactic calculus and residuated categories, Mathematical Systems Theory, vol. 2 (1968), pp. 287-318.
15. YIANNIS MOSCHOVAKIS, English as a programming language, Tarski Lecture 2, (March 5, 2008) available at http://www.math.ucla.edu/~ynm/lectures.htm.
16. -, What is an algorithm?, Mathematics unlimited (B. Engquist and W. Schmid, editors), Springer-Verlag, 2001, pp. 919-936.
17. CHRISTOS PAPADMITRIOU, Algorithms, games, and the internet, Proceedings of the 33rd annual ACM Symposium on Theory of Computing (STOC), ACM, 2001, pp. 749-753.
18. LITERATE PROGRAMS, Merge sort, web site, http://en.literateprograms.org/Merge.sort(C).
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.
21. PETR VOPěnka, Mathematics in the alternative set theory, Teubner Verlag, 1979.
22. WIKIPEDIA, Euclidean algorithm, 2008, web site, http://www.answers.com/topic/euclidean-algorithm?cat=technology (viewed on January 27, 2008.).
23. NOSON YANOFSKY, Towards a definition of an algorithm, preprint, 2006, arXiv:math/0602053.