Unfolding-based Partial Order Reduction

Partial order reduction (POR) and net unfoldings are two alternative methods to tackle state-space explosion caused by concurrency. In this paper, we propose the combination of both approaches in an effort to combine their strengths. We first define, for an abstract execution model, unfolding semantics parameterized over an arbitrary independence relation. Based on it, our main contribution is a novel stateless POR algorithm that explores at most one execution per Mazurkiewicz trace, and in general, can explore exponentially fewer, thus achieving a form of super-optimality. Furthermore, our unfolding-based POR copes with non-terminating executions and incorporates state-caching. Over benchmarks with busy-waits, among others, our experiments show a dramatic reduction in the number of executions when compared to a state-of-the-art DPOR.Comment: Long version of a paper with the same title appeared on the proceedings of CONCUR 201

Characterization of Reachable Attractors Using Petri Net Unfoldings

International audienceAttractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion. In this paper, we present a new algorithm that exploits the concurrency between transitions of parallel acting components in order to reduce the search space. The algorithm relies on Petri net unfoldings that can be used to compute a compact representation of the dynamics. We illustrate the applicability of the algorithm with Petri net models of cell signalling and regulation networks, Boolean and multi-valued. The proposed approach aims at being complementary to existing methods for deriving the attractors of Boolean models, while being %so far more generic since it applies to any safe Petri net

Petri Games: Synthesis of Distributed Systems with Causal Memory

We present a new multiplayer game model for the interaction and the flow of information in a distributed system. The players are tokens on a Petri net. As long as the players move in independent parts of the net, they do not know of each other; when they synchronize at a joint transition, each player gets informed of the causal history of the other player. We show that for Petri games with a single environment player and an arbitrary bounded number of system players, deciding the existence of a safety strategy for the system players is EXPTIME-complete.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Goal-Driven Unfolding of Petri Nets

Unfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain all the reachable markings. In this paper we are interested in reachability of a single given marking, called the goal. We propose an algorithm for computing a finite prefix of the unfolding of a 1-safe Petri net that preserves all minimal configurations reaching this goal. Our algorithm combines the unfolding technique with on-the-fly model reduction by static analysis aiming at avoiding the exploration of branches which are not needed for reaching the goal. We present some experimental results

An Improved Construction of Petri Net Unfoldings

Petri nets are a well-known model language for concurrent systems. The unfolding of a Petri net is an acyclic net bisimilar to the original one. Because it is acyclic, it admits simpler decision problems though it is in general larger than the net. In this paper, we revisit the problem of efficiently constructing an unfolding. We propose a new method that avoids computing the concurrency relation and therefore uses less memory than some other methods but still represents a good time-space tradeoff. We implemented the approach and report on experiments

Conflict Equivalence of Branching Processes

International audienceFor concurrent and large systems, specification step is a crucial point. Combinatory explosion is a limit that can be encountered when a state space exploration is driven on large specification modeled with Petri nets. Considering bounded Petri nets, technics like unfolding can be a way to cope with this problem. This paper is a first attempt to present an axiomatic model to produce the set of processes of unfoldings into a canonic form. This canonic form allows to define a conflict equivalence

Directed unfolding of petri nets

The key to efficient on-the-fly reachability analysis based on unfolding is to focus the expansion of the finite prefix towards the desired marking. However, current unfolding strategies typically equate to blind (breadth-first) search. They do not exploit the knowledge of the marking that is sought, merely entertaining the hope that the road to it will be short. This paper investigates directed unfolding, which exploits problem-specific information in the form of a heuristic function to guide the unfolding towards the desired marking. In the unfolding context, heuristic values are estimates of the distance between configurations. We show that suitable heuristics can be automatically extracted from the original net. We prove that unfolding can rely on heuristic search strategies while preserving the finiteness and completeness of the generated prefix, and in some cases, the optimality of the firing sequence produced. We also establish that the size of the prefix obtained with a useful class of heuristics is never worse than that obtained by blind unfolding. Experimental results demonstrate that directed unfolding scales up to problems that were previously out of reach of the unfolding technique