Verification Techniques for TSO-Relaxed Programs

Knowing the extent to which we rely on technology one may think that correct programs are nowadays the norm. Unfortunately, this is far from the truth. Luckily, possible reasons why program correctness is difficult often come hand in hand with some solutions. Consider concurrent program correctness under Sequential Consistency (SC). Under SC, instructions of each program's concurrent component are executed atomically and in order. By using logic to represent correctness specifications, model checking provides a successful solution to concurrent program verification under SC. Alas, SC’s atomicity assumptions do not reflect the reality of hardware architectures. Total Store Order (TSO) is a less common memory model implemented in SPARC and in Intel x86 multiprocessors that relaxes the SC constraints. While the architecturally de-atomized execution of stores under TSO speeds up program execution, it also complicates program verification. To be precise, due to TSO’s unbounded store buffers, a program’s semantics under TSO might be infinite. This, for example, turns reachability under SC (a PSPACE-complete task) into a non-primitive-recursive-complete problem under TSO. This thesis develops verification techniques targeting TSO-relaxed programs. To be precise, we present under- and over-approximating heuristics for checking reachability in TSO-relaxed programs as well as state-reducing methods for speeding up such heuristics. In a first contribution, we propose an algorithm to check reachability of TSO-relaxed programs lazily. The under-approximating refinement algorithm uses auxiliary variables to simulate TSO’s buffers along instruction sequences suggested by an oracle. The oracle’s deciding characteristic is that if it returns the empty sequence then the program’s SC- and TSO-reachable states are the same. Secondly, we propose several approaches to over-approximate TSO buffers. Combined in a refinement algorithm, these approaches can be used to determine safety with respect to TSO reachability for a large class of TSO-relaxed programs. On the more technical side, we prove that checking reachability is decidable when TSO buffers are approximated by multisets with tracked per address last-added-values. Finally, we analyze how the explored state space can be reduced when checking TSO and SC reachability. Intuitively, through the viewpoint of Shasha-and-Snir-like traces, we exploit the structure of program instructions to explain several state-space reducing methods including dynamic and cartesian partial order reduction