🤖 AI Summary
To address the challenge of complete detection of unsafe states in infinite-state systems—particularly when state evolution exhibits regularity—this paper proposes a novel top-down regular model checking paradigm. The core method starts from the set of all configurations and computes the intersection of all inductive b-invariants (i.e., CNF formulas with at most b clauses) to over-approximate the reachable set, thereby avoiding non-termination inherent in traditional iterative widening. Theoretical contributions include: (i) proving that, for any b ≥ 0, the intersection of all b-invariants is always a regular language, and a corresponding finite automaton can be effectively constructed; and (ii) establishing that safety verification is PSPACE-complete when b = 1. Experimental evaluation demonstrates that small values of b (e.g., b = 1 or 2) suffice to efficiently verify safety for multiple benchmark systems.
📝 Abstract
Regular model checking is a technique for the verification of infinite-state systems whose configurations can be represented as finite words over a suitable alphabet. The form we are studying applies to systems whose set of initial configurations is regular, and whose transition relation is captured by a length-preserving transducer. To verify safety properties, regular model checking iteratively computes automata recognizing increasingly larger regular sets of reachable configurations, and checks if they contain unsafe configurations. Since this procedure often does not terminate, acceleration, abstraction, and widening techniques have been developed to compute a regular superset of the reachable configurations. In this paper, we develop a complementary procedure. Instead of approaching the set of reachable configurations from below, we start with the set of all configurations and approach it from above. We use that the set of reachable configurations is equal to the intersection of all inductive invariants of the system. Since this intersection is non-regular in general, we introduce b-invariants, defined as those representable by CNF-formulas with at most b clauses. We prove that, for every $bgeq0$, the intersection of all inductive b-invariants is regular, and we construct an automaton recognizing it. We show that whether this automaton accepts some unsafe configuration is in EXPSPACE for every $bgeq0$, and PSPACE-complete for b=1. Finally, we study how large must b be to prove safety properties of a number of benchmarks.