An Incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic

In this paper we present a new decision procedure for the satisfiability of Linear Arithmetic Logic (LAL), i.e. boolean combinations of prepositional variables and linear constraints over numerical variables. Our approach is based on the well known integration of a propositional SAT procedure with theory deciders, enhanced in the following ways. First, our procedure relies on an incremental solver for linear arithmetic, that is able to exploit the fact that it is repeatedly called to analyze sequences of increasingly large sets of constraints. Reasoning in the theory of LA interacts with the boolean top level by means of a stack-based interface, that enables the top level to add constraints, set points of backtracking, and backjump, without restarting the procedure from scratch at every call. Sets of inconsistent constraints are found and used to drive backjumping and learning at the boolean level, and theory atoms that are consequences of the current partial assignment are inferred. S...