Paper:

# Infinite Computation in the Equivalent Transformation Model

## Hiroshi Mabuchi^{*}, Kiyoshi Akama^{**}, Hidekatsu Koike^{***},

and Katsunori Miura^{**}

^{*}Faculty of Software and Information Science, Iwate Prefectural University, Iwate, Japan

^{**}Information Initiative Center, Hokkaido University, Sapporo, Japan

^{***}Faculty of Social Information, Sapporo Gakuin University, Ebetsu, Hokkaido, Japan

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11 No.2, pp. 176-186, 2007.

- [1] M. A. Nait Abdallah, “On the Interpretation of Infinite Computatations in Logic Programming,” in 11th International Colloquium on Automata, Languages and Programming, ICALP’84, J. Paredaens (Ed.), pp. 358-370, Vol.172 of Lecture Notes in Computer Science, Springer-Verlag, 1984.
- [2] K. Akama, T. Shimizu, and E. Miyamoto, “Solving Problems by Equivalent Transformation of Declarative Programs,” Journal of Japanese Society for Artificial Intelligence, Vol.13, No.6, pp. 944-952, 1998.
- [3] K. Akama, Y. Shigeta, and E. Miyamoto, “Changing Knowledge Representation Systems by Expanding Specialization Systems,” Journal of Japanese Society for Artificial Intelligence, Vol.13, No.1, pp. 131-138, 1998.
- [4] K. Akama, Y. Kawaguchi, and E. Miyamoto, “Equivalent Transformation for Equality Constraints on Multiset Domains,” Journal of Japanese Society for Artificial Intelligence, Vol.13, No.3, pp. 395-403, 1998.
- [5] K. Akama, Y. Shigeta, and E. Miyamoto, “Solving Logical Problems by Equivalent Transformation (1) –A Theoretical Foundation–,” Journal of Japanese Society for Artificial Intelligence, Vol.13, No.6, pp. 928-935, 1998.
- [6] K. Akama, E. Nantajeewarawat, and H. Koike, “A Class of Rewriting Rules and Reverse Transformation for Rule-Based Equivalent Transformation,” Electronic Notes in Theoretical Computer Science, 59, No.4, pp. 1-16, 2001.
- [7] K. R. Apt and van M. H. Emden, “Contributions to the Theory of Logic Programming,” JACM, Vol.29, No.3, pp. 841-862, 1982.
- [8] P. Boizumault, “A Classical Implementation for PrologII,” Lecture Notes in Computer Science, Vol.213, pp. 262-273, Springer-Verlag, 1986.
- [9] W. F. Clocksin and C. S. Mellish, “Programming in Prolog,” 2nd edition, Springer-Verlag, 1984.
- [10] A. Colmerauer, “Prolog and Infinite Trees,” Logic Programming, Academic Press, 1982.
- [11] F. S. de Boer, A. Di Pierro, and C. Palamidessi, “Nondeterminism and Infinite Computations in Constraint Programming,” Theoretical Computer Science, 151, pp. 37-78, 1995.
- [12] W. G. Golson, “Toward a Declarative Semantics for Infinite Objects in Logic Programming,” Journal of Logic Programming, 5, pp. 151-164, 1988.
- [13] J. Hein, “Completions of Perpetual Logic Programs,” Theoretical Computer Science, 99, pp. 65-78, 1992.
- [14] J. Jaffar and J. L. Lassez, “Constraint Logic Programming,” in Conference Record of the Fourteenth Annual ACMSymposium on Principles of Programming Languages, pp. 111-119, 1987.
- [15] G. Levi and C. Palamidessi, “Contributions to the Semantics of Logic Perpetual Processes,” Acta Informatica, 25(6): pp. 691-711, 1988.
- [16] J. W. Lloyd, “Foundations of Logic Programming,” 2nd edition, p. 212, Springer-Verlag, 1987.
- [17] H. Mabuchi, K. Akama, Y. Shigeta, and H. Koike, “Equivalent Transformation of Member Constraints on Interval-Variable Domain,” Journal of Japanese Society for Artificial Intelligence, Vol.17, No.1 C, pp. 23-31, 2002.
- [18] M. Jaume, “On Greatest Fixpoint Semantics of Logic Programming,” J. Logic and Computation, Vol.12, No.2, pp. 321-342, 2002.
- [19] S. Nystrom and B. Jonsson, “Indeterminate Concurrent Constraint Programming: A Fixpoint Semantics for Non-Terminating Computations,” in Logic Programming – Proceedings of the 1993 International Symposium, D. Miller (Ed.), pp. 335-352, The MIT Press, 1993.
- [20] V. A. Saraswat, M. C. Rinard, and P. Panangaden, “Semantic Foundations of Concurrent Constraint Programming,” in Conference Record of the Eighteenth Annual ACM Symposium on Principles of Programming Languages, pp. 333-352, 1991.
- [21] D. A. Turner, “An Overview of Miranda,” SIGPLAN Notices, Vol.21, No.12, pp. 158-166, 1986.
- [22] T. Yoshida, K. Akama, and E. Miyamoto, “Representation and Computation Using First-order Logical Constraints,” Proc. of the 5th International Conference on Information Systems Analysis and Synthesis, 1999.

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