Quasi-Optimal Partial Order Reduction

Abstract

A dynamic partial order reduction (DPOR) algorithm is optimal when it always explores at most one representative per Mazurkiewicz trace. Existing literature suggests that the reduction obtained by the non-optimal, state-of-the-art Source-DPOR (SDPOR) algorithm is comparable to optimal DPOR. We show the first program 4 with O(n) Mazurkiewicz traces where SDPOR explores O(2 n ) redundant schedules. We furthermore identify the cause of this blow-up as an NP-hard problem. Our main contribution is a new approach, called Quasi-Optimal POR, that can arbitrarily approximate an optimal exploration using a provided constant k. We present an implementation of our method in a new tool called Dpu using specialised data structures. Experiments with Dpu, including Debian packages, show that optimality is achieved with low values of k, outperforming state-of-the-art tools.if a ∈ enabl (s) and s a − → s , then a ∈ enabl (s) iff a ∈ enabl (s ); and if a, a ∈ enabl (s), then there is a state s such that s a.a −−→ s and s a .a −−→ s .

Unfolding-Based Dynamic Partial Order Reduction of Asynchronous Distributed Programs

“…Parametric Unfolding Semantics. Given an LTS T and an independence relation I , one can build a prime event structure E such that each linearization of a maximal (for inclusion) configuration represents an execution in T , and conversely, to each Mazurkiewicz trace in T corresponds a configuration in E [13].…”

“…In order to avoid sleep-set blocked executions (SSB) and obtain the optimality of DPOR, the function Alt(C , D ∪{e}) has to solve an NP-complete problem [13]: find a subset J of U that can be used for backtracking, conflicts with all D ∪ {e} thus necessarily leading to a configuration C ∪J that is not already visited. In this case en(C ) ⊆ D can then be replaced by en(C ) = ∅ in line 5.…”

“…In [16] the authors propose unfolding-based DPOR (UDPOR), an optimal DPOR method combining the strengths of PORs and unfoldings with the notion of alternatives. The approach is generalized [13] with a notion of kpartial alternative allowing to balance between optimal DPOR and sometimes more efficient sub-optimal DPOR.…”

“…Already defining a correct independence relation from this formal model is difficult, due to the variety and complex semantics of actions. In addition, making UDPOR and in particular the computation of unfoldings and extensions efficient cannot directly rely on solutions of [13], which are tuned for concurrent programs with only mutexes, thus clever algorithms need to be designed. For now we prototyped our solutions in a simplified context, but we target the Sim-Grid tool which allows to run HPC code (in particular MPI) in a simulation environment [5].…”

Constrained Dynamic Partial Order Reduction

“…For the previous example, [16] needs to explore five executions: r.p.q and r.q.p, are equivalent because p and q do not have any observer. Another improvement orthogonal to ours is to inspect dependencies over chains of events, as in [17,19].…”