A Formally Verified SMT Approach to True Concurrency

Many problems related to distributed and parallel systems, such as scheduling and optimisation, are computationally hard, thereby justifying the adoption of SMT solvers. The latter provide standard arithmetic as interpreted functions, naturally leading to express concurrent executions as a linearly-ordered sequentialisation (or interleaving) of events, which have an obvious correspondence with integer segments and therefore permit to take advantage of such arithmetical capabilities. However, there are alternative semantic approaches (also known as true concurrent) not imposing the extra step of interleaving events, which brings the question of how to computationally exploit SMT solvers in these approaches. This paper presents a solution to this problem, and introduces a metric, made possible by adopting a true concurrent paradigm, which relates mutually distinct solutions of a family of distributed optimisation problems. We also contribute an original, computational definition of degree of parallelism, which we compare with the existing ones. Finally, we use theorem proving to formally certify a basic correctness property of our true concurrent approach.