Local First Search — A New Paradigm for Partial Order Reductions

Black Box Unfolding with Local First Search

“…The framework is thus kept as a level of generality so as to apply to a wide variety of system descriptions, not just Petri nets or products of automata. For further motivating examples of this choice, see [NHZL01].…”

“…Such properties depend on a single component of the system so that one should be able to identify equivalent classes of global states and tackle the state explosion while checking their possible reachability. The Local First Search approach [NHZL01] gives a combinatorial criterion that shows how to explore a reduced and yet locally complete subset of states in an efficient way. Based on observations linked to the Strahler number of trees [Str52], this new technique characterizes concurrent executions which may be cut off from the exploration while checking any local property.…”

“…Moreover, the complicated computation of possible extensions for the construction of the complete finite prefix (see [KK01] for an extended discussion) is fully avoided by our approach, at the price of a bigger result (but, as explained in [NHZL01], not necessarily higher computational cost). In addition, it relies solely on abstract characteristics of concurrency within the system, not on a particular representation like Petri nets.…”

“…In Section 3, we formalize the notion of a local property in the context of asynchronous transition systems. In Section 4, we rephrase the main theorem of [NHZL01] in terms of traces and give a summary of its application to the verification of local properties. The main contribution is in Section 5, the development of a locally complete finite subsystem and the proof of its completeness for the local reachability problem.…”

A nice labelling for tree-like event structures of degree 3

“…Some model checkers -see for example [16] and [17] -make explicit use of trace theory and of the theory of partially ordered sets to represent the state space of a concurrent system. The combinatorics of posets is then exploited to achieve an efficient exploration of the global states of concurrent systems [18,19,20]. Thus, having a solid theoretical understanding of such combinatorics is a prerequisite and a complement for designing efficient algorithms for these kind of tools.…”