Complexity aspects of web services composition

The web service composition problem can be stated as follows: given a finite state machine M , representing a service business protocol, and a set of finite state machines R, representing the business protocols of existing services, the question is to check whether there is a simulation relation between M and the shuffle product closure of R. In fact the shuffle product is a subclass of the communication free petri net and basic parallel processes, for which the same problem of simulation is known to be 2-Exptime-hard. This paper studies the impact of several parameters on the complexity of this problem. We show that the problem is Exptime-complete if we bound either: (i) the number of instances of services in R that can be used in a composition, or (ii) the number of the so-called hybrid states in the finite state machines of R. Moreover, for the particular case where the bound of the hybrid states of the finite state machines of R is set to 2, we show that the composition problem is in 3-Exptime