Grammars and Automata to Optimize Chain Logic Queries

The critical problem of finding efficient implementations for recursive queries with bound arguments offers many open challenges of practical and theoretical import. In particular, there is a need to find methods that are effective for the general case, such as non-linear programs, as well as for specialized cases, such as left-recursive linear programs. In this paper, we propose a novel approach that solves this problem for chain queries, i.e., for queries where bindings are propagated from arguments in the head to arguments in the tail of the rules, in a chain-like fashion. The method, called pushdown method, is based on the fact that a chain query can have associated a context-free language and a pushdown automaton recognizing this language can be emulated by rewriting the query as a particular factorized left-linear program. The proposed method generalizes and unifies previous techniques such as the 'counting' and 'right-, left-, mixed-linear' methods. It also succeeds in reducing many non-linear programs to query-equivalent linear ones.