State-Transition Computation Models and Program Correctness Thereon

Kiyoshi Akama; Ekawit Nantajeewarawat

doi:10.20965/jaciii.2007.p1250

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JACIII Vol.11 No.10 pp. 1250-1261

doi: 10.20965/jaciii.2007.p1250

(2007)

Paper:

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State-Transition Computation Models and Program Correctness Thereon

Kiyoshi Akama^* and Ekawit Nantajeewarawat^**

^*Division of Large-Scale Computational Systems, Information Initiative Center, Hokkaido University, Kita 11 Nishi 5, Kita-ku, Sapporo, Hokkaido 060-0811, Japan

^**Computer Science Program, Sirindhorn International Institute of Technology, Thammasat University, Rangsit Campus, P.O. Box 22, Thammasat-Rangsit Post Office, Pathumthani 12121, Thailand

Received:

October 30, 2006

Accepted:

February 1, 2007

Published:

December 20, 2007

Keywords:

state-transition computation model, program correctness, embedding mapping

Abstract

The common framework for formalizing state-transition computation models we present is based on a general theory for studying the interrelationship of specifications, programs, computation, and program correctness. We establish a necessary and sufficient condition for program correctness for this class of computation models and demonstrate framework application by formalizing, as its instances, two concrete examples of state-transition computation models – NAT and D-rule. We compare their correct-program spaces by introducing the embedding mapping concept.

Cite this article as:

K. Akama and E. Nantajeewarawat, “State-Transition Computation Models and Program Correctness Thereon,” J. Adv. Comput. Intell. Intell. Inform., Vol.11 No.10, pp. 1250-1261, 2007.

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References

[1] K. Akama and E. Nantajeewarawat, “Formalization of Computation Models in View of Program Synthesis,” in Proc. the 4th Int. Conf. on Intelligent Technologies, Chiang Mai, Thailand, pp. 507-516, 2003.
[2] J. W. Lloyd, “Foundations of Logic Programming,” second, extended edition, Springer-Verlag, 1987.
[3] T. Frühwirth, “Theory and Practice of Constraint Handling Rules,” Journal of Logic Programming, Vol.37, pp. 95-138, 1998.
[4] J. Jaffar, M. Maher, K. Marriott, and P. Stuckey, “The Semantics of Constraint Logic Programs,” Journal of Logic Programming, Vol.37, pp. 1-46, 1998.
[5] R. Bird, “Introduction to Functional Programming,” second edition, Prentice Hall, 1998.
[6] K. Akama, Y. Shigeta, and E. Miyamoto, “Solving Logical Problems by Equivalent Transformation – A Theoretical Foundation,” Journal of the Japanese Society for Artificial Intelligence, Vol.13, pp. 928-935, 1998.
[7] K. Akama and E. Nantajeewarawat, “Formalization of the Equivalent Transformation Computation Model,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.3, pp. 245-259, 2006.
[8] Y. Gurevich, “Sequential Abstract-State Machines Capture Sequential Algorithms,” ACM Transactions on Computational Logic, Vol.1, No.1, pp. 77-111, 2000.
[9] E. Börger and R. Stärk, “Abstract State Machines: A Method for High-level System Design and Analysis,” Springer-Verlag, 2003.
[10] C. A. Petri, “Nets, Times and Spaces,” Theoretical Computer Science, Vol.153, pp. 3-48, 1996.
[11] N. Dershowitz and J.-P. Jouannaud, “Rewriting Systems,” in Handbook of Theoretical Computer Science, Vol.B: Formal Methods and Semantics, North-Holland, pp. 243-320, 1990.
[12] E. Nantajeewarawat, K. Akama, and H. Koike, “Expanding Transformation: A Basis for Correctness Verification of Rewriting Rules,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.5, pp. 478-490, 2007.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] K. Akama and E. Nantajeewarawat, “Formalization of Computation Models in View of Program Synthesis,” in Proc. the 4th Int. Conf. on Intelligent Technologies, Chiang Mai, Thailand, pp. 507-516, 2003.

[2] [2] J. W. Lloyd, “Foundations of Logic Programming,” second, extended edition, Springer-Verlag, 1987.

[3] [3] T. Frühwirth, “Theory and Practice of Constraint Handling Rules,” Journal of Logic Programming, Vol.37, pp. 95-138, 1998.

[4] [4] J. Jaffar, M. Maher, K. Marriott, and P. Stuckey, “The Semantics of Constraint Logic Programs,” Journal of Logic Programming, Vol.37, pp. 1-46, 1998.

[5] [5] R. Bird, “Introduction to Functional Programming,” second edition, Prentice Hall, 1998.

[6] [6] K. Akama, Y. Shigeta, and E. Miyamoto, “Solving Logical Problems by Equivalent Transformation – A Theoretical Foundation,” Journal of the Japanese Society for Artificial Intelligence, Vol.13, pp. 928-935, 1998.

[7] [7] K. Akama and E. Nantajeewarawat, “Formalization of the Equivalent Transformation Computation Model,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.3, pp. 245-259, 2006.

[8] [8] Y. Gurevich, “Sequential Abstract-State Machines Capture Sequential Algorithms,” ACM Transactions on Computational Logic, Vol.1, No.1, pp. 77-111, 2000.

[9] [9] E. Börger and R. Stärk, “Abstract State Machines: A Method for High-level System Design and Analysis,” Springer-Verlag, 2003.

[10] [10] C. A. Petri, “Nets, Times and Spaces,” Theoretical Computer Science, Vol.153, pp. 3-48, 1996.

[11] [11] N. Dershowitz and J.-P. Jouannaud, “Rewriting Systems,” in Handbook of Theoretical Computer Science, Vol.B: Formal Methods and Semantics, North-Holland, pp. 243-320, 1990.

[12] [12] E. Nantajeewarawat, K. Akama, and H. Koike, “Expanding Transformation: A Basis for Correctness Verification of Rewriting Rules,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.5, pp. 478-490, 2007.

State-Transition Computation Models and Program Correctness Thereon

Kiyoshi Akama* and Ekawit Nantajeewarawat**

Kiyoshi Akama^* and Ekawit Nantajeewarawat^**