Paper:

# Design of Nondeterministic Program Termination Based on the Equivalent Transformation Computation Model

## Itaru Takarajima^{*}, Kiyoshi Akama^{**}, Ikumi Imani^{***},

and Hiroshi Mabuchi^{****}

^{*}Department of Commerce, Nagoya Gakuin University, 1350 Kami-Shinano, Seto, Aichi 480-1298, Japan

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

^{***}Department of Foreign Studies, Nagoya Gakuin University, Seto, Japan

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

We studied the termination of nondeterministic programs, which play an important, basic role in program synthesis, and provide a foundation for proving program termination. The class of programs we consider here is based on the *equivalent transformation (ET)* computation model. Computation with this model involves the succesive application of rules to sets of clauses. Since the ET model has more expressive terms and rules than other programming languages, program termination is difficult to prove: we must take into account all possible changes of terms made by various rules. We propose a sufficient condition of ET program termination that proves termination by checking each rule in a given program. We also provide an algorithm for this check.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.10, No.3, pp. 349-361, 2006.

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