Black Box Unfolding with Local First Search

Abstract

McMillan's unfolding approach to the reachability problem in 1-safe Petri nets and its later improvements by Esparza-Römer-Vogler have proven in practice as a very effective method to avoid stateexplosion. This method computes a complete finite prefix of the infinite branching process of a net. On the other hand, the Local First Search approach (LFS) was recently introduced as a new partial order reduction technique which characterizes a restricted subset of configurations that need to be explored to check local properties. In this paper we amalgamate the two approaches: We combine the reduction criterion of LFS with the notions of an adequate order and cutoff events essential to the unfolding approach. As a result, our new LFS method computes a reduced transition system without the problem of state duplication (present in the original LFS). Since it works for any transition system with an independence relation, this black box partial unfolding remains more general than the unfolding of Petri nets. Experiments show that the combination gives improved reductions compared to the original LFS.

The Implementation of Mazurkiewicz Traces in POEM

“…Local First Search (LFS) [2,13] is a partial order method to seach for local properties. For a property ϕ, a visible action causes the system to move from a state not satisfying ϕ to a state satisfying it, or vice versa.…”

“…Given that most of the mentioned specification languages use some kind of interleaving model of automata with shared variables and certain kinds of communication, POEM uses a common data structure as an abstract specification language (it does not have a concrete syntax) that allows comparatively easy translation of specification languages into a unique metalanguage. This paper focuses on the design and the implementation details of traces in POEM, and presents how to extend it to implement Local First Search [2,13]. Moreover, We show the improvement of time consuming of Event Zone approach [11] by combining it with the trace structure.…”

Stronger Reduction Criteria for Local First Search

“…Among these methods, Local First Search (LFS) [11,1] is specialized for the complete search for local properties, i.e. properties that can only be modified by dependent transitions.…”

“…In [11], a first method for exploiting this criterion was given, which however did not guarantee that the number of states actually explored would be inferior to the global number of states. In [1] in contrast, the LFS-bound is combined with ideas from McMillan unfoldings [4] to obtain a breadth first search based algorithm that is complete and never explores the same state twice. For a number of benchmarks, it was observed that (asymptotically) LFS with the unfolding approach gives decent reductions where the stubborn set method [17], the ample set [13] and related methods give only very weak reductions.…”

“…On the whole, we thus obtain a modular proof of the original theorem and stronger reduction criteria. Efficient exploration algorithms have been implemented using the technique from [1].…”