计算ac统一子完备集的双指数复杂度

[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science Pub Date : 1992-06-22 DOI:10.1109/LICS.1992.185515

D. Kapur, P. Narendran

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引用次数: 54

摘要

给出了一种计算包含结合能交换函数符号的两项统一子的完备集的算法。本文基于作者1986年提出的一种不确定性算法，证明了结合-交换统一的np完备性。该算法易于理解，且易于建立终止。它的复杂性很容易分析，并且在输入项的大小上显示为双指数。分析还表明，两个输入项的统一子的完备集的大小有一个双指数上界。由于存在一类简单的结合-交换统一问题，这些问题具有大小为双指数的完整统一子集，因此该算法在此意义上的复杂度顺序是最优的

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Double-exponential complexity of computing a complete set of AC-unifiers

An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, and its termination can be easily established. Its complexity is easily analyzed and shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense.<>

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[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science

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