Speedup of Recognizable Trace Languages

Traces have been defined by A.Mazurkiewicz in order to modelize concurrent processes. The decomposition of a trace in Foata normal form gives the “best” parallel execution of a trace. We define naturally the speedup of a trace as the quotient of its sequential execution time by its parallel execution time. We generalize this definition to trace languages and we prove that this speedup can be computed in a modular way for any recognizable trace language.