On Variable Selection in SAT-LP-based Bounded Model Checking of Linear Hybrid Automata

One approach for the verification of embedded systems, where discrete control is embedded in a continuous environment, is bounded model checking of linear hybrid automata. As a decision procedure within this context, a combination of a propositional SAT-solver and an LP-solver can be used. For such combined SAT-LP solvers, it is, among others, an open question how a robust, i.e., reliable, variable selection heuristics should be designed. In this work we investigate the design of such heuristics taking into account (1) the algorithmic structure of the combined SAT-LP-solver, and (2) efficiency issues in form of a counter-based design that adapts the popular concept of the VSIDS heuristics of Chaff. An empirical analysis of our framework shows (1) the importance of guard variables related to real-valued constraints and (2) reveals an ambiguity between the number of calls of the LP-solver and the time used by the LP-solver. As a result, we propose a simple, but efficient, variable selection heuristics that takes our observations into account and experimentally overcomes the limitations of existing ones.