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The Specialization of Programs by Theorem Proving
http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80756
title: The Specialization of Programs by Theorem Proving abstract: Suppose a program P is written to accept a set of inputs I. If we are only interested in a nonempty subset $I^ * $ of I, we usually can simplify P to another program $P^ * $ such that $P^ * $ runs faster on $I^ * $ than P does. The problem of specialization is to find such $P^ * $. In this paper, the program P and the input $I^ * $ will be specified by axioms. Using these axioms, we can obtain $P^ * $ from P through theorem-proving techniques.
<br>An Algorithm to Generate Prime Implicants and Its Applications to the Selection Problem
http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80757
title: An Algorithm to Generate Prime Implicants and Its Applications to the Selection Problem abstract: In this paper, the algorithm to generate prime implicants presented in Ref. 5 is extended to a new algorithm. The new algorithm does not require the Boolean function to be in conjunctive normal form and is complete in the sense that it generates all the prime implicants. The author also shows that this new algorithm can be used to efficiently solve the selection problem . By using this algorithm, the original selection problem can be solved by a branch-and-bound approach which avoids an exhaustive search of the solution space and reduces the amount of necessary calculations.
<br>Fuzzy Logic and the Resolution Principle
http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80758
title: Fuzzy Logic and the Resolution Principle abstract: The relationship between fuzzy logic and two-valued logic in the context of the first order predicate calctflus is discussed. It is proved that if every clause in a set of clauses is somethblg more than a "half-truth" and the most reliable clause has truth-value a and the most unreliable clause has truth-value b, then we are guaranteed that all the logical con- sequences obtained by repeatedly applying the resolution principle will have truth-value between a and b. The significance of this theorem is also discussed.
<br>Some Properties of Fuzzy Logic
http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/80759
title: Some Properties of Fuzzy Logic abstract: In this paper, the fuzzy set [Zadeh (1965)] is viewed as a multivalued logic with a
continuum of truth values in the interval [0, 1]. The concepts of in- consistency, validity, prime implicant and prime implicate are extended to fuzzy logic and various properties
of these notions m the context of fuzzy logic are established. It is proved that a formula is valid (inconsistent) in fuzzy logic iff it is valid (inconsistent) in two-valued logic. An algorithm that generates fuzzy prime implicants (implicates) is introduced. A proof of the completeness of this algorithm is also given.
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