Partial-order Checking with Unfolding for Linear Temporal Properties

Unfolding can tackle the path-explosion problem caused by concurrency. Traditional unfolding generation faces an NP-complete problem when adding events to the unfolding structure, which also exists in the case of verifying linear temporal logic (LTL). The reason is that it is necessary to enumerate possible concurrent event combinations after adding an event. Many state-of-the-art methods optimally explore unfolding-based structure (called event structure) by a tree-like structure, which should be constructed on the event structure with complete conflict and causal relations. However, a synchronization of a Petri net and the Buchi representation of LTL as a folded net can not represent complete conflict and causal relations. Thus, it is difficult to apply such a tree-like structure directly on the folded net. To resolve this difficulty, we propose a new method, called partial-order checking with unfolding, to verify LTL based on PDNet (program dependence net). We define an exploration tree with a new notion of delayed transitions, which is different from the existing tree-like structure. It improves the unfolding generation by avoiding all possible event combinations. Then, we propose an algorithm to simultaneously construct the exploration tree while generating the unfolding structure, as well as checking LTL. We implement a tool PUPER for concurrent programs with POSIX threads. It improves traditional unfolding generations via our exploration tree-based algorithms and shows better performance than SPIN and DiVine on the used benchmarks.