Complexity of nonrecursive logic programs with complex values

values should be treated. There are two major approaches. We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so WC study the complexity of nonrecursive queries. By complcx values we understand values such as trees, finite sets, and multlscts. Due to the well-known correspondence between relational query languages and datalog, our results can be considered as results about relational query languages with complex values. The paper gives a complete complexity classification of the SUCCESS problem for nonrecursive logic programs over trees depending on the underlying signature, presence of negation, and range restrictedness. We also prove several results about finite sets and multisets. 1. In constmint logic programming [41,42] and constraa’nt databases [33] any value is identified by the set of constraints true on this value. The addition of a new type of values requires the addition of new constraint predicates. A similar approach to relational query languages was also considered in [lo]. 2. Another approach to adding complex values, which can be called structuml, requires that values be represented by means of their structure. For example, to represent sets one may enrich the language with constant 0 to denote the empty set and the set constructor {sit} denoting the addition of an element s to the set t. Then the set (tl,. . . , {tll . . . {tnlO}. . .}. t,,} will be denoted by the term The only changes to the semantics of logic programming are the changes in the treatment of equality, since new predicate symbols are not free constructors. Such an approach is considered in a number of papers, for example [25,37,9,50,22,21,19].