Expressive power and data complexity of nonrecursive query languages for lists and trees

Abstract

We extend the traditional query languages by primitives for handling lists and trees. Our main results characterize the expressive power and data complexity of the following extended languages: (1) relational algebra with lists and trees, (2) nonrecursive Datalog with lists and trees, (3) nonrecursive Prolog with lists and trees, (4) first-order logic over lists and trees. Languages (2)-(4) turn out to have the same expressive power; their range-restricted fragments have the same expressive power as (1). Every query in these languages is a boolean combination of range-restricted queries. We also prove that these query languages have polynomial data complexity under any `reasonable' encoding of inputs. Furthermore, under a natural encoding of inputs, languages (2)-(4) have the same expressive power as first-order logic over finite structures, therefore their data complexity is in AC0. Thus, the use of lists and trees in nonrecursive query languages gives no gain in the expressiveness. This contrasts with a huge difference between the nonelementary program complexity of extended languages (2)-(4) and the PSPACE program complexity of their relational counterparts. Our results partly explain why lists and trees are not so widely used in nonrecursive query languages as other collection types.