Efficient verification of concurrent systems using local-analysis-based approximations and SAT solving

Abstract

This work develops a type of local analysis that can prove concurrent systems deadlock free. As opposed to examining the overall behaviour of a system, local analysis consists of examining the behaviour of small parts of the system to yield a given property. We analyse pairs of interacting components to approximate system reachability and propose a new sound but incomplete/approximate framework that checks deadlock and local-deadlock freedom. By replacing exact reachability by this approximation, it looks for deadlock (or local-deadlock) candidates, namely, blocked (locally-blocked) system states that lie within our approximation. This characterisation improves on the precision of current approximate techniques. In particular, it can tackle non-hereditary deadlock-free systems, namely, deadlock-free systems that have a deadlocking subsystem. These are neglected by most approximate techniques. Furthermore, we demonstrate how SAT checkers can be used to efficiently implement our framework, which, typically, scales better than current techniques for deadlock-freedom analysis. This is demonstrated by a series of practical experiments.

Efficient Verification of Concurrent Systems Using Synchronisation Analysis and SAT/SMT Solving

“…In [6], we have shown that the problems of checking both deadlock-and local-deadlockfreedom are PSPACE -complete. Intuitively, the need to explore induced LTSs and their state-space explosion can be seen as the cause for this problem's membership of this complexity class.…”

“…In the proof to Theorem 2 in [6], we present a construction that, in polynomial time, transforms a given supercombinator machine S into a machine T ′ (S) for which the blocked predicate for S coincides with the locally-blocked predicate for T ′ (S). Furthermore, this translation has no impact in any of the reachability approximations that we present here.…”

“…We built upon our SAT-checking approach proposed for detecting Pair candidates in [6] to create an efficient implementation for PairStatic. We implement our framework using SAT formulas P airStatic R and LocalP airStatic R , and SMT formulas P airStatic D and LocalP airStatic D .…”

“…Our formulas reuse sub-formulas State, Blocked, LocallyBlocked and Reach 2 proposed in [6]. To make this paper self-contained, we reintroduce (slightly simplified versions of) them here.…”

“…Since our framework tackles NP -hard problems, we build on the SAT encoding proposed for Pair to create efficiently checkable SAT and SMT encodings of our verification problems. We extend our DeadlOx tool [6] to implement this new framework. Furthermore, we demonstrate by a series of practical experiments that this tool is more accurate than (and as efficient as) similar approximate techniques.…”