Canonization for disjoint unions of theories

Canonization for Disjoint Unions of Theories

If there exist efficient procedures (canonizers) for reducing terms of two first-order theories to canonical form, can one use them to construct such a procedure for terms of the disjoint union of the two theories? We prove this is possible whenever the original theories are convex. As an application, we prove that algorithms for solving equations in the two theories (solvers) cannot be combine...

Canonization for Disjoint Unions of Theories

Unions of non-disjoint theories and combinations of satisfiability procedures

Non-Disjoint Unions of Theories and Combinations of Satis ability Procedures: First Results

In this paper we outline a theoretical framework for the combination of decision procedures for the satis ability of constraints with respect to a constraint theory. We describe a general combination method which, given a procedure that decides constraint satis ability with respect to a constraint theory T1 and one that decides constraint satis ability with respect to a constraint theory T2, is...

The Complexity of Unions of Disjoint Sets

This paper is motivated by the open question whether the union of two disjoint NPcomplete sets always is NP-complete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities. Moreover, we approach the main question in a more general way: We analyze the scope of the complexity of unions o...