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Loop schemata

Published: 03 May 1971 Publication History

Abstract

We define a class of program schemata arising from the subrecursive programming language Loop. In this preliminary report on Loop schemata we show how to assign functional expressions to these schemata (as one aspect of the problem of assigning meaning to these programs), and we outline a solution to the schemata equivalence problem. Schemata equivalence is reduced to questions about formal expressions. Certain subcases of the problem are easily shown solvable, and although we claim that the general problem is solvable, we do not present the complete solution here because of its complexity.

References

[1]
Constable, R L and A B Borodin On the efficiency of programs in subrecursive formalisms, IEE Conf. Record, Symposium in Switching and Automata Theory, 1970, 60-67. (to appear in JACM)
[2]
Ianov, I The logical schemes of algorithms, Problems of Cybernetics I, 82-140 (English translation), 1960.
[3]
Meyer, A and D M Ritchie The complexity of Loop programs, Proc. 22, National ACM Conference, 1967, 465-470.
[4]
Milner, R Program schemes and recursive function theory, Machine Intelligence, 1970, 39-58.
[5]
Minsky, M Computation, finite and infinite, Prentice-Hall, Englewood Cliffs.
[6]
Paterson, M S Program schemata, Machine Intelligence 3, 1968, 1931.
[7]
Paterson, M S Equivalence problems in a model of computation, Artificial Intelligence, Technical Memo (153 pages) No. 1, M.I.T., 1970.
[8]
Rogers, H Theory of Recursive Functions and Effective Computability, New York, 1967.

Cited By

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  • (1975)Function iteration logics and flowchart schemataFunktion-Wiederholungslogiken und FlußdiagrammschemataComputing10.1007/BF0224643314:3(285-312)Online publication date: Sep-1975
  • (1972)Subrecursive program schemata I & II(I. Undecidable equivalence problems, II. Decidable equivalence problems)Proceedings of the fourth annual ACM symposium on Theory of computing10.1145/800152.804892(1-17)Online publication date: 1-May-1972

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Published In

cover image ACM Conferences
STOC '71: Proceedings of the third annual ACM symposium on Theory of computing
May 1971
270 pages
ISBN:9781450374644
DOI:10.1145/800157
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 May 1971

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Author Tags

  1. Algol
  2. Computable function
  3. Equivalence problem
  4. Functional
  5. General recursive functional
  6. Loop language
  7. Primitive recursive function
  8. Program
  9. Program schemata
  10. Subrecursive programming language
  11. Universal programming language
  12. Unsolvability

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Acceptance Rates

STOC '71 Paper Acceptance Rate 23 of 50 submissions, 46%;
Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

View all
  • (1975)Function iteration logics and flowchart schemataFunktion-Wiederholungslogiken und FlußdiagrammschemataComputing10.1007/BF0224643314:3(285-312)Online publication date: Sep-1975
  • (1972)Subrecursive program schemata I & II(I. Undecidable equivalence problems, II. Decidable equivalence problems)Proceedings of the fourth annual ACM symposium on Theory of computing10.1145/800152.804892(1-17)Online publication date: 1-May-1972

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