Tractable and intractable second-order matching problems

  • Authors:

  • Kouichi Hirata;Keizo Yamada;Masateru Harao

  • Affiliations:

  • Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan

  • Venue:
  • COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
  • Year:
  • 1999

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Abstract

The second-order matching problem is the problem of determining, for a finite set {〈ti, si〉 | i ∈ I} of pairs of a second-order term ti and a first-order closed term si, called a matching expression, whether or not there exists a substitution σ such that tiσ = si for each i ∈ I. It is well-known that the second-order matching problem is NP-complete. In this paper, we introduce the following restrictions of a matching expression: k-ary, k-fv, predicate, ground, and function-free. Then, we show that the second-order matching problem is NP-complete for a unary predicate, a unary ground, a ternary function-free predicate, a binary function-free ground, and an 1-fv predicate matching expressions, while it is solvable in polynomial time for a binary function-free predicate, a unary function-free, a k-fv function-free (k ≥ 0), and a ground predicate matching expressions.