Automatic Synthesis of Minimal Algorithms from Samples of Their Behavior

  • P. G. Raulefs
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 83)

Abstract

An efficient implementation of an exhaustive search program synthesizing a minimal representation of algorithms from samples of their behavior is presented. As finding specific machines performing given tasks crucially depends on notions of simulation assumed, concepts of operational simulation and equivalence of algorithms are given. Applications to program synthesis, describing the structure of data sets, texture recognition, systems diagnosis, and grammatical inference are indicated.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BARTELS-WIED 71]
    Bartels, P.H. and Wied, G.L., “Tumor cell diagnosis based on stochastic properties of digitized images”, Proc. Two-Dimensional Digital Signal Processing Conf., Columbia, Mo., Oct. 1971.Google Scholar
  2. [BIERMANN 71]
    Biermann, A.W., “On the Inference of Turing Machines from Sample Computations”, A.I. Memo AIM-152/CS-241, Computer Science Dept., Stanford Univ., Oct. 1971. Revised version: J. Artificial Intelligence: 3 (1972), 181–198.MATHMathSciNetGoogle Scholar
  3. [BIERMANN-FELDMAN 70]
    Biermann, A.W. und Feldman, J.A., “On the Synthesis of Finite-State Acceptors”, A.I. Memo AIM-114.1, Computer Science Dept., Stanford Univ., Aug. 1970.Revised version: IEEE:C-21 (1972), 592–596.Google Scholar
  4. [BIERMANN-FELDMAN 72]
    Biermann, A.W. and Feldman, J.A., “A Survey of Results in Grammatical Inference”, Proc. Conf. Frontiers of Pattern Recognition, Honululu, Jan. 1971.Google Scholar
  5. [BLUM 67 a]
    Blum, M., “A Machine-Independent Theory of the Com¬plexity of Recursive Functions”, JACM: 14 (1967), 322–336.CrossRefMATHGoogle Scholar
  6. [BLUM 67 b]
    Blum, M., “On the Size of Machines”, Inf. and Contr.: 11 (1967) 257–265.CrossRefMATHGoogle Scholar
  7. [FELDMAN 69]
    Feldman, J.A.,“Some Decidability Results on Grammatical Inference and Complexity”, A.I. Memo AIM-93.1, Computer Science Dept., Stanford Univ., Aug. 1969.Revised version: Inf. and Contr.: 20 (1972) 244–262.MATHGoogle Scholar
  8. [HWA-WRIGHTSON 73]
    Hwa, J.C.-H. and Wrightson, G., “Synthese von Turing maschinen aus endlichen Mengen von ner Bericht, Inst. f. Informatik I, Univ. Karlsruhe, 1973 (in preparation)Google Scholar
  9. [PAGER 69]
    Pager, D., “On the Problem of Finding Minimal Programs for Tables”, Inf. and Contr.: 14 (1969) 550–554.CrossRefMATHGoogle Scholar
  10. [PAGER 70]
    Pager, D., “On the Efficiency of Algorithms”, JACM: 17 (1970) 708–714.CrossRefMATHMathSciNetGoogle Scholar
  11. [RAULEFS 73a]
    Raulefs, P., “KASAS-Karlsruhe Automatic Synthesis of Algorithms System. Project Specifications”, Interner Bericht, Inst. f. Informatik I, Universität Karlsruhe, 1973 (in preparation).Google Scholar
  12. [RAULEFS 73b]
    Raulefs, P., “Operational Simulation and Equivalence of Algorithms”, Interner Bericht, Inät. f. Informatik I, Univ. Karlsruhe, 1973 (in preparation).Google Scholar
  13. [SALOMAA 69]
    Salomaa, A., “Theory of Automata”, Pergamom Press, 1969.Google Scholar
  14. [SHANK 71]
    Shank, H.S., “Records of Turing Machines”, MST: 5 (1971)50–55.Google Scholar
  15. [SHANNON 56]
    Shannon, C.E., “A Universal Turing Machine with Two Internal States”, in Automata Studies, Princeton Univ. Press, 1956.Google Scholar
  16. [SCHMITT 68]
    Schmitt, A., “Über die Berechnung minimaler Turing¬maschinen und anderer minimaler Systeme”, EIK: 4 (1968) 318–326.Google Scholar
  17. [WEGNER 72]
    Wegner, P., “Operational Semantics of Programming Languages”, Proc. ACM Conf. Proving Assertions about Programs, Las Cruces, N.M., Jan. 1972 (SIGPLAN Notices: 7.1 / SIGACT News: 14).Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1973

Authors and Affiliations

  • P. G. Raulefs

There are no affiliations available

Personalised recommendations