Satisfiability of Boolean Formulas over Linear Constraints

Test ing the sat is f iabi l i ty of a Boolean fo rmu la over l inear constraints is not a s imple ma t ter. Ex is t ing AI systems handle tha t k ind o f problems w i t h a general proof method for their Boolean parts and a separate module for comb in ing l inear constraints. On the contrary, t rad i t i ona l operat ions research methods need the prob lem to be t ransformed, and solved w i t h a M ixed Integer Linear P rog ramming a lgo r i t hm. B o t h approaches appear to be improvable i f no early separat ion is in t roduced between the logical and numer ica l parts. In this case, comb ina to r ia l explosion can be dramat ica l l y reduced thanks to efficient looking-ahead techniques and learning methods.