Sanchari Sil

R. Govind, S. Krishna, Sanchari Sil et al.

In a seminal work, Gibbons and Korach studied the complexity of deciding whether an observed sequence of reads and writes of a multi-threaded program admits a sequentially consistent interleaving. They showed the problem to be NP-hard even under strong syntactic restrictions. More recently, Chakraborty et al. considered the problem for weak memory models and proved that NP-hardness remains even when the number of threads, the number of memory locations, and the value domain are all bounded. In this paper we revisit the problem for the release-acquire variants of the C11 memory model. Our main positive result is that consistency testing can be done in polynomial-time when each memory location is written by at most one thread (multiple readers are allowed). Notably, this restriction is already NP-hard for sequential consistency. We complement this upper bound with tight hardness results: the problem is NP-hard when two threads may write to the same location, and allowing three writers per location rules out 2^{o(k)}.n^{O(1)} algorithms under the Exponential Time Hypothesis, where k denotes the number of threads, and n the number of memory operations.

R. Govind, S. Krishna, Sanchari Sil et al.

Gibbons and Korach studied a fundamental problem in 1997: given an observed sequence of reads and writes of a multi-threaded program, does there exist an interleaving which is sequentially consistent? Apart from applications in testing shared memory implementations, a procedure for this problem is employed in Dynamic Partial-Order-Reduction (DPOR) algorithms. The problem is known to be NP-hard even when different syntactic parameters are kept bounded. In this paper, we consider a restriction on the kind of interleaving required: does there exist a sequentially-consistent interleaving with at most π preemptions? Empirical evidence suggests that several bugs manifest within a few preemptive switches. This motivates us to investigate the problem under bounded preemptions. Our results exhibit a trichotomy: the problem lends to a polynomial-time algorithm for the class of single-writer programs where for each variable, there is a single thread writing to it; it becomes NP-hard for two-writer programs and finally, for three-writer programs, we get a conditional lower bound under the Exponential-Time-Hypothesis. When the number of preemptions π is not bounded, we show the problem to be W[1]-hard, and hence unlikely to be fixed-parameter-tractable with parameter π.