Abstract. It is well known that through code instrumentation, a distributed system's finite execution can generate a finite trace as a partially ordered set of events. We motivate the need to use LTL model-checking on sequences and not on traces as defined by Diekert and Gastin, to validate distributed control systems executions, abstracted by such traces, and present an efficient symbolic algorithm to do the job. It uses the standard method proposed by Vardi and Wolper, which from the LTL formula, builds a monitor that accepts all the bad sequences. We show that, given a monitor and a trace, the problem to check that both the monitor and the trace have a common sequence is NP-complete in the number of concurrent processes. Our method explores the possible configurations symbolically, since it handles sets of configurations. Moreover, it uses techniques similar to the partial order reduction, to avoid exploring as many execution interleavings as possible. It works very well in practice, compared to the standard exploration method, with or without partial order reduction (which, in practice, does not work well here).

We study the formal verification of programs written in d SL, an extension of the standard ST language used to program industrial controllers. It proposes a trade off between industrial and formal verification worlds. The main advantage of d SL is to provide a transparent code distribution through low level communication mechanisms. The behavior of the synthesized distributed system can therefore be formally modeled, easily monitored and formally verified. The verification of a d SL program, realized with the Spin tool, is eased by the definition of a lattice of models linked with a simulation relation preserving next-free LTL formulae. We show that, although d SL is an industrial programming language, it gives the possibility to verify systems designed with it. We illustrate the benefit of our approach with a simple control system of two canal locks.

Abstract. We present the problem of statically distributing instructions of a common programming language, a problem which we prove equivalent to the multiterminal cut problem. We design efficient shrinkage techniques which allow to reduce the size of an instance in such a way that optimal solutions are preserved. We design and evaluate a fast local heuristics that yields remarkably good results compared to a well known 2 − 2 k approximation algorithm. The use of the shrinkage criterion allows us to increase the size of the instances solved exactly, or to augments the precision of any particular heuristics.