A quantitative study of fork-join processes with non-deterministic choice: Application to the statistical exploration of the state-space

•We study concurrent programs with non-deterministic choice, loops and a fork-join style of coordination under the lens of combinatorics.•We propose a framework, based on analytic combinatorics, allowing to analyse their quantitative aspects.•We develop efficient algorithms aimed at the statistical exploration of their state-space: uniform samplers of bounded executions and prefixes.•Our algorithms work on the syntax of the programs and do not require the explicit construction of the state-space. We study concurrent processes with non-deterministic choice, loops and a fork-join style of coordination under the lens of combinatorics. As a starting point, we interpret these processes as combinatorial structures. We propose a framework, based on analytic combinatorics, allowing to analyse their quantitative aspects such as the average number of execution paths induced by the choice operator, or the proportion of executions of a process with respect to its number of execution prefixes. Building on this theoretical investigation, we develop efficient algorithms aimed at the statistical exploration of their state-space. The first algorithm is a uniform random sampler of bounded executions, providing a good default exploration strategy. The second algorithm is a uniform random sampler of execution prefixes of a given bounded length, allowing to bias the exploration in a controlled manner. The fundamental characteristics of these algorithms is that they work on the syntax of the programs and do not require the explicit construction of the state-space.