NP Datalog: a logic language for NP search and optimization queries

This paper presents a logic language, called NP Datalog for NP search and optimization problems. The 'search' language extends stratified Datalog with constraints and partition rules defining (nondeterministically) partition of relations. NP optimization problems are then formulated by adding a max (or min) construct to select the solution (stable model) which maximizes (resp., minimizes) the result of a polynomial function applied to the answer relation. We show that NP Datalog queries can be easily evaluated by translating them into ILOG programs which are next solved by means of the ILOG OPL Studio suite. To prove the effectiveness of our proposal, we have implemented a module, written in Sicstus Prolog, which takes in input a NP Datalog query and outputs an equivalent ILOG program. Several experiments comparing the computation of queries by different logic systems have been also performed.