On the Completeness of Verifying Message Passing Programs Under Bounded Asynchrony

Abstract

We address the problem of verifying message passing programs, defined as a set of parallel processes communicating through unbounded FIFO buffers. We introduce a bounded analysis that explores a special type of computations, called k-synchronous. These computations can be viewed as (unbounded) sequences of interaction phases, each phase allowing at most k send actions (by different processes), followed by a sequence of receives corresponding to sends in the same phase. We give a procedure for deciding k-synchronizability of a program, i.e., whether every computation is equivalent (has the same happens-before relation) to one of its k-synchronous computations. We also show that reachability over k-synchronous computations and checking k-synchronizability are both PSPACE-complete. Furthermore, we introduce a class of programs called flow-bounded for which the problem of deciding whether there exists a k > 0 for which the program is k-synchronizable, is decidable.

On the k-synchronizability of Systems

“…We show, now, that the reachability problem is decidable for k-synchronizable systems. While proving this result, we have to face several non-trivial aspects of causal delivery that were missed in [4] and that require a completely new approach. We write sT r k (S) to denote the set {msc(e) | e ∈ asEx(S) and msc(e) is k-synchronous}.…”

“…Following standard terminology, we say that a subset U ⊆ V of vertices is a strongly connected component (SCC) of a given graph (V, →) if between any two vertices v, v ′ ∈ U , there exist two oriented paths v → * v ′ and v ′ → * v. The statement below fixes some issues with Theorem 1 in [4] (see Section 6 for a detailed discussion).…”

“…In a recent work [4], Bouajjani et al introduced the notion of k-synchronizable system of finite state machines communicating through mailboxes. Intuitively, a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be chopped into a succession of k-bounded interaction phases.…”

“…Another problem is the membership problem for the subclass of k-synchronizable systems: for a given k and a given system of communicating finite state machines, is this system k-synchronizable? The main result in [4] is that this problem is decidable. However, again, the proof of this result contains an important flaw at the very first step that breaks all subsequent developments; as a consequence, the algorithm given in [4] produces both false positives and false negatives.…”

“…The main result in [4] is that this problem is decidable. However, again, the proof of this result contains an important flaw at the very first step that breaks all subsequent developments; as a consequence, the algorithm given in [4] produces both false positives and false negatives.…”