Complexities of Homomorphism and Isomorphism for Definite Logic Programs

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 clause. For each definite program clause a ← a1, ..., an ∈ P it implies that φ(a) ← φ(a1), ..., φ(an) is a program clauses 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).

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