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As an alternative to logic-based query languages for recursive queries, we are investigating a graphical query language called G+, which allows, among other things, easy formulation of certain queries involving simple paths in directed graphs. This led us to study whether such queries are expressible in DATALOG, the language of function-free Horn clauses. Since some G+ queries are NP-hard, and all DATALOG queries are polynomial time computable, the answer appears to be negative. However, it would be interesting to have proof techniques and tools for settling such questions with certainty. The objective of this paper is the development of one such tool, inductive pebble games, based on a normal form for DATALOG programs derived here, and its relationship to Alternating Turing Machine computations. As an application, we sketch a proof that the query “find all pairs of nodes connected by a directed simple path of even length” cannot be expressed in DATALOG.

Inductive pebble games and the expressive power of datalog