论文信息 - Decidability of the Existential Theory of Infinite Terms with Subterm Relation

Decidability of the Existential Theory of Infinite Terms with Subterm Relation

We examine the problem of solving equations, inequalities, and atomic formulas built on the subterm relation in algebras of rational and infinite terms (trees). We prove that this problem is decidable for any such algebra in a finite signature S with possible new free constants. Moreover, even in presence of subterm relation, the existential theory of rational trees is the same as the existential theory of infinite trees. We leave out the easier case where S has no symbols of arity greater than one. When S has only a symbol of arity greater than one, the decision procedure is different in the two cases where the algebra of rational or infinite trees does or does not contain new free constants.

Sauro Tulipani

[1] B. Courcelle. Fundamental properties of infinite trees , 1983 .

[2] Michael J. Maher. Complete axiomatizations of the algebras of finite, rational and infinite trees , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[3] Melvin Fitting,et al. A Kripke-Kleene Semantics for Logic Programs , 1985, J. Log. Program..

[4] Hubert Comon-Lundh,et al. Equational Problems and Disunification , 1989, J. Symb. Comput..

[5] S. Tulipani,et al. Quantifier elimination for infinite terms , 1991, Arch. Math. Log..

[6] K. N. Venkataraman,et al. Decidability of the purely existential fragment of the theory of term algebras , 1987, JACM.

[7] Ralf Treinen,et al. A New Method for Undecidability Proofs of First Order Theories , 1990, FSTTCS.

[8] Derek C. Oppen. Reasoning About Recursively Defined Data Structures , 1980, J. ACM.

[9] J. W. Lloyd,et al. Foundations of logic programming; (2nd extended ed.) , 1987 .

[10] H. Comon. SOLVING SYMBOLIC ORDERING CONSTRAINTS , 1990 .

[11] Frank M. Hawrusik,et al. A View of Computability on Term Algebras , 1983, J. Comput. Syst. Sci..

[12] Alain Colmerauer,et al. Equations and Inequations on Finite and Infinite Trees , 1984, FGCS.

[13] Martin Davis. On the number of solutions of Diophantine equations , 1972 .

[14] Kenneth Kunen,et al. Negation in Logic Programming , 1987, J. Log. Program..