On the Complexity of Bounded Context Switching

Bounded context switching (BCS) is an under-approximate method for finding violations to safety properties in shared-memory concurrent programs. Technically, BCS is a reachability problem that is known to be NP-complete. Our contribution is a parameterized analysis of BCS. The first result is an algorithm that solves BCS when parameterized by the number of context switches (cs) and the size of the memory (m) in O∗(mcs · 2). This is achieved by creating instances of the easier problem Shuff which we solve via fast subset convolution. We also present a lower bound for BCS of the form mo(cs/ log(cs)), based on the exponential time hypothesis. Interestingly, the gap is closely related to a conjecture that has been open since FOCS’07. Further, we prove that BCS admits no polynomial kernel. Next, we introduce a measure, called scheduling dimension, that captures the complexity of schedules. We study BCS parameterized by the scheduling dimension (sdim) and show that it can be solved in O∗((2m)4sdim4t), where t is the number of threads. We consider variants of the problem for which we obtain (matching) upper and lower bounds. 1998 ACM Subject Classification D.2.4 Software/Program Verification, F.2.2 Nonnumerical Algorithms and Problems