Complexities of Homomorphism and Isomorphism for Definite Logic Programs

Abstract

A homomorphism ϕ of logic programs from P to P' is a function mapping Atoms(P) to Atoms(P') and it preserves complements and program clauses. For each definite program clause a ← a1,...,an ∈ P it implies that ϕ(a) ← ϕ(a1),..., ϕ(an) is a program clause of P'. A homomorphism ϕ is an isomorphism if ϕ is a bijection. In this paper, the complexity of the decision problems on homomorphism and isomorphism for definite logic programs is studied. It is shown that the homomorphism problem (HOM-LP) for definite logic programs is NP-complete, and the isomorphism problem (ISO-LP) is equivalent to the graph isomorphism problem (GI).