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On and/or schemes

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Book cover Mathematical Foundations of Computer Science 1980 (MFCS 1980)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 88))

Abstract

A computational model, based on and/or subgoaling, is described. It is shown that various models of computation, such as recursive program schemes, decision trees and combinational networks, are naturally embedded in the and/or language. These observations pose some interesting questions for further research. As a first result in the metatheory of and/or schemes, we prove a normal form theorem showing that with the addition of “auxiliary variables”, every and/or scheme is strongly equivalent to one with “and/or depth” equal to 1.

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VI. References

  1. Borodin, A.B. On Relating Time and Space to Size and Depth. SIAM J. on Computing, 6, pp. 733–744, 1977.

    Google Scholar 

  2. Chandra, A.K. Degrees of Translatability and Canonical Forms in Program Schemas. Proceedings of the 6th ACM Symp. on Theory of Computing, pp. 1–12, 1974.

    Google Scholar 

  3. Cooper, D.C. Bohm and Jacopini's Reduction of Flow Charts. Comm. of the ACM, Vol. 10, pp. 463, 473. Aug. 1967.

    Google Scholar 

  4. Chandra, A.K. D. Kozen and L. Stockmeyer. Alternation. To appear in J. of the ACM.

    Google Scholar 

  5. Culik, K. The Cyclomatic Number and the Normal Number of Programs. SIGPLAN Notices, 14;4, April 1979.

    Google Scholar 

  6. Dijkstra, E.W. A Discipline of Programming. Prentice-Hall, Inc., Englewood Cliffs, NJ. 1976.

    Google Scholar 

  7. Elshoff, J.L. and M. Marcotty. On the Use of the Cyclomatic Number to Measure Program Complexity. SIGPLAN Notices, 13;12, Dec. 1978.

    Google Scholar 

  8. Engeler, E. Structure and Meaning of Elementary Programs. Proc. Symp. on Semantics of Algorithmic Languages. Lecture Notes in Mathematics, Vol. 188, Springer-Verlag, 1971, pp. 89–101.

    Google Scholar 

  9. Greibach, S.A. Theory of Program Structures: Schemes, Semantics, Verification. Lecture Notes in Computer Science, Vol.36, Springer-Verlag. 1974.

    Google Scholar 

  10. Hansen, W.J. Measurement of Program Complexity by the Pair (Cyclomatic Number, Operator Count). SIGPLAN Notices, 13; 3, Mar. 1978.

    Google Scholar 

  11. Harel, D. And/Or Programs: A New Approach to Structured Programming. ACM Transactions on Prog. Lang. and Syst., Vol. 2, No. 1, Jan. 1980, pp. 1–17.

    Google Scholar 

  12. Harel, D. On Folk Theorems. Comm. of the ACM. 23:7, July 1980.

    Google Scholar 

  13. Hill, F. J. and Z. Narabi. Extending Second Generation AHPL Software to Accomodate AHPL III. Proceedings IEEE 4th International Symp. on Computer Hardware Description Languages. Palo Alto, CA, Oct. 1979.

    Google Scholar 

  14. Knuth, D. The Art of Computer Programming: Sorting and Searching. Addison-Wesley, Inc., 1973.

    Google Scholar 

  15. Ladner, R. E. and M. J. Fischer. Parallel Prefix Computation. International Conf. on Parallel Processing, pp. 218–223, 1977.

    Google Scholar 

  16. Manna, Z. Mathematical Theory of Computation. McGraw Hill, 1974.

    Google Scholar 

  17. McCabe, T.J. A Complexity Measure. IEEE Trans. on Software Engineering. SE-2; 4, Dec. 1976.

    Google Scholar 

  18. Myers, G.J. An Extension to the Cyclomatic Measure of Program Complexity. SIGPLAN Notices, 12; 10, Oct. 1977.

    Google Scholar 

  19. Peterson, G.L. Upper Bounds on the Size of Formulae for Symmetric Boolean Functions. Revised TR-78-03-01, Dept. of Computer Science, Univ. of Washington, Seattle. May 1978.

    Google Scholar 

  20. Pippenger, N. On Simultaneous Resource Bounds. Proceedings 20th IEEE Symp. on Foundations of Computer Science. San Juan, Puerto Rico, Oct. 1979.

    Google Scholar 

  21. Pippenger, N. and M. J. Fischer. Relations Among Complexity Measures. J. of the ACM, 26; 2, April 1979.

    Google Scholar 

  22. Ruzzo, W.L. On Uniform Circuit Complexity. Proceedings 20th IEEE Symp. on Foundations of Computer Science. San Juan, Puerto Rico, Oct. 1979.

    Google Scholar 

  23. Schnorr, C. P. The Network Complexity and the Turing Maching Complexity of Finite Functions. Acta Informatica, 7 pp. 95–107 1976.

    Google Scholar 

  24. Schonhage, A., M. Paterson and N. Pippenger. Finding the Median. J. of Comp. and System Sciences, Vol.13, No.2, Oct. 1976.

    Google Scholar 

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Author notes

  1. David Harel

    Present address: Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel

Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, New York

    David Harel

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  1. David Harel
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P. Dembiński

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© 1980 Springer-Verlag Berlin Heidelberg

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Harel, D. (1980). On and/or schemes. In: Dembiński, P. (eds) Mathematical Foundations of Computer Science 1980. MFCS 1980. Lecture Notes in Computer Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022509

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  • DOI: https://doi.org/10.1007/BFb0022509

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10027-0

  • Online ISBN: 978-3-540-38194-5

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