Counterexample Guided Invariant Discovery for Parameterized Cache Coherence Verification

Abstract

Abstract. We propose a heuristic-based method for discovering inductive invariants in the parameterized verification of safety properties. The promise of the method stems from powerful heuristics we have identified for verifying the cache coherence of directory based protocols. The heuristics are based on syntactic analysis of counterexamples generated during verification, combined with simple static analysis of the predicates involved in the counterexamples to construct and refine inductive invariants. The heuristics were effective in filtering irrelevant predicates as well as keeping the sizes of the generated inductive invariants small. Contributions are: (i) the method is an efficient strategy for discovering inductive invariants for practical verification; (ii) the heuristics scaled smoothly from two small to one large cache coherence protocol (of complexity similar to commercial cache coherence protocols); (iii) the heuristics generate relevant auxiliary invariants which are easily verifiable in few seconds; and (iv) the method does not depend on special verification frameworks and so can be adapted for other verification tools. The case studies include German, FLASH, and a new protocol called German-Ring. The properties verified include mutual exclusion and data consistency.

ParaVerifier: An Automatic Framework for Proving Parameterized Cache Coherence Protocols

“…Within paraVerifier, our automatic framework for parameterized verification of cache coherence protocol, (1) instead of directly proving the invariants of a protocol by induction, we propose a general proof method based on the consistency lemma to decompose the proof goal into a number of small ones; (2) instead of proving the decomposed subgoals by hand, we automatically generate proofs for them based on the information computed in a small protocol instance. 8 As we demonstrate in this work, combining theorem proving with automatic proof generation is promising in the field of formal verification of industrial protocols. Theorem proving can guarantee the rigorousness of the verification results, while automatic proof generation can release the burden of human interaction.…”

“…Theorem proving can guarantee the rigorousness of the verification results, while automatic proof generation can release the burden of human interaction. 8 Technical details of paraVerifier will be made available in a technical report.…”

“…Verification of parameterized systems (e.g., see [1,2,3,4,5,6,7,8,9,10,11]) is interesting in the area of formal methods, mainly due to the practical importance of such systems. Parameterized systems exist in many application domains, including cache coherence protocols, security systems, and network communication protocols.…”

“…Many works have focused on the construction of a set of auxiliary invariants, for example, see [4,6,8,10,11]. However, the theoretical foundation of these techniques and their soundness proofs are often only discussed in the respective papers.…”

Invariants for Parameterised Boolean Equation Systems

“…Historically, the main use of invariants is in proofs of safety properties like data consistency or mutual exclusion [2,21]; liveness properties, on the other hand, are better supported by variant notions like the ranking functions [3,6]. These capture the monotonic dynamics of a property rather than its stability through process execution.…”