Precise Thread-Modular Verification

Abstract

Abstract. Thread-modular verification is a promising approach for the verification of concurrent programs. Its high efficiency is achieved by abstracting the interaction between threads. The resulting polynomial complexity (in the number of threads) has its price: many interesting concurrent programs cannot be handled due to the imprecision of the abstraction. We propose a new abstraction algorithm for threadmodular verification that offers both high degree precision and polynomial complexity. Our algorithm is based on a new abstraction domain that combines Cartesian abstraction with exception sets, which allow one to handle particular thread interactions precisely. Our experimental results demonstrate the practical applicability of the algorithm.

Thread-Modular Counterexample-Guided Abstraction Refinement

“…E.g. for the example of Mueller we have k = 3, m = 1, an unspecified n. This class extends the class presented in [23] by allowing variably long critical sections.…”

“…Second, the Cartesian abstraction used by the thread-modular approach is refined by adding (1, 1, 0, B, D) (or, alternatively (1, 1, 0, C, C)) to the so-called exception set [23]. The states in the exception set are excluded from the Cartesian abstraction, thus refining it.…”

“…We automate our previous work on exception sets [23] (which requires user interaction) by exploiting spurious counterexamples.…”

“…However, the precision loss caused by multi-threaded Cartesian abstraction often leads to inconclusive results. In [23], we presented a method for refining multi-threaded Cartesian abstraction that is based on the so-called exception sets. An exception set is, roughly, a set of states that is excluded from the approximation of an abstraction.…”

“…Since each exception set has a polynomial-size maximized form, each refinement phase is polynomial-time by [23]. The number of refinement phases is also polynomial, so the total runtime is polynomial.…”