Search and optimization problems in datalog

Abstract

This paper analyzes the ability of DATALOG languages toexpress search and optimization problems. It is first shown that NP search problems can be formulated as unstratified DATALOG queries under non-deterministic stable model semantics so that each stable model corresponds to a possible solution. NP optimization problems are then formulated by adding a max (or min) construct to select the stable model (thus, the solution) which maximizes (resp., minimizes) the result of a polynomial function applied to the answer relation. In order to enable a simpler and more intuitive formulation for search and optimization problems, it is introduced a DATALOG language in which the use of stable model semantics is disciplined to refrain from abstruse forms of unstratified negation. The core of our language is stratified negation extended with two constructs allowing nondeterministic selections and with query goals enforcing conditions to be satisfied by stable models. The language is modular as the level of expressivity can be tuned and selected by means of a suitable use of the above constructs, thus capturing significant subclasses of search and optimization queries. © Springer-Verlag Berlin Heidelberg 2002.