By Susumu Hayashi, Ryosuke Sumitomo (auth.), Jieh Hsiang, Atsushi Ohori (eds.)
This publication constitutes the refereed complaints of the 4th Asian Computing technological know-how convention, ASIAN'98, held in Manila, The Philippines, in December 1998.
The 17 revised complete papers awarded have been conscientiously reviewed and chosen from a complete of forty three submissions. additionally incorporated are a couple of invited contributions. one of the issues lined are automatic deduction, evidence concept, rewriting platforms, application semantics, allotted processing, algorithms, and graph-theoretical points.
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Extra info for Advances in Computing Science ASIAN 98: 4th Asian Computing Science Conference Manila, The Philippines, December 8–10, 1998 Proceedings
But somehow, it has not been emphasized in the automated deduction literature. No special heuristics for reasoning about tables implementing finite functions have been studied. In this paper, we have emphasized exploiting the entries in a table for doing case analysis in mechanizing proof attempts of conjecture involving the table. The number of cases generated by the proposed approach is the same as that based on case analyses on indices in the worst case. Given, indices drawn from domains with cardinality d1 and d2 , the total number of cases generated by index based case analyses is d1 ∗ d2 .
The entry based case analyses considers all possible values of partial remainders while verifying the invariant, and not just the boundary values as done in [1,8]. It is encouraging that by exploiting simple characteristics of tables such as sparsity, a comprehensive correctness proof simpler than the one based on manual abstrac- 40 Deepak Kapur and M. Subramaniam tion [1,8] can be automatically obtained, while eliminating the scope of errors introduced by manual abstraction. The proofs reported in  using the PVS system are more general.
The validity of the invariant (C3) is reduced to showing that the above 9 constraints on indices up, ud are satisfied for different quotient digit values. These constraints can be checked exhaustively by explicitly plugging in various values of up, ud which give rise to each of quotient digits. Below, we show how structure about the indices can be exploited further to check these constraints without having to explicitly substitute values of up and ud. Since the above constraints are simple inequalities, and indices are subranges over numbers, this information can be used to simplify this check as illustrated below.
Advances in Computing Science ASIAN 98: 4th Asian Computing Science Conference Manila, The Philippines, December 8–10, 1998 Proceedings by Susumu Hayashi, Ryosuke Sumitomo (auth.), Jieh Hsiang, Atsushi Ohori (eds.)