The Complexity of Predicting Atomicity Violations

• Authors: Azadeh Farzan;P. Madhusudan
• Venue: TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
• Year: 2009

We study the prediction of runs that violate atomicity from a single run, or from a regular or pushdown model of a concurrent program. When prediction ignores all synchronization, we show predicting from a single run (or from a regular model) is solvable in time O (n + k .c k ) where n is the length of the run (or the size of the regular model), k is the number of threads, and c is a constant. This is a significant improvement from the simple $O(n^k\cdot 2^{k^2})$ algorithm that results from building a global automaton and monitoring it. We also show that, surprisingly, the problem is decidable for model-checking recursive concurrent programs without synchronizations. Our results use a novel notion of a profile : we extract profiles from each thread locally and compositionally combine their effects to predict atomicity violations. For threads synchronizing using a set of locks $\mathcal{L}$, we show that prediction from runs and regular models can be done in time $O(n^k\cdot 2^{|\mathcal{L}|\cdot \log k+{k^2}})$. Notice that we are unable to remove the factor k from the exponent on n in this case. However, we show that a faster algorithm is unlikely : more precisely, we show that prediction for regular programs is unlikely to be fixed-parameter tractable in the parameters $(k,|\mathcal{L}|)$ by proving it is W [1]-hard. We also show, not surprisingly, that prediction of atomicity violations on recursive models communicating using locks is undecidable.