The complexity of recursive constraint satisfaction problems

Abstract

For Anil Nerode, our teacher, mentor and friend, on his 75th birthday, in recognition of his guidance in logic and life MSC: 03D15 03D25 03D80 Keywords:Recursive constraint satisfaction problems Recursive trees Degrees of solutions a b s t r a c tWe investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem.