Infinite-state backward exploration of Boolean broadcast programs

Abstract

Assertion checking for non-recursive unbounded-thread Boolean programs can be performed in principle by converting the program into an infinite-state transition system such as a Petri net and subjecting the system to a coverability check, for which sound and complete algorithms exist. Said conversion adds, however, an additional heavy burden to these already expensive algorithms, as the number of system states is exponential in the size of the program. Our solution to this problem avoids the construction of a Petri net and instead applies the coverability algorithm directly to the Boolean program. A challenge is that, in the presence of advanced communication primitives such as broadcasts, the coverability algorithm proceeds backwards, requiring a backward execution of the program. The benefit of avoiding the up-front transition system construction is that "what you see is what you pay": only system states backward-reachable from the target state are generated, often resulting in dramatic savings. We demonstrate this using Boolean programs constructed by the SatAbs predicate abstraction engine.