Fairness of components in system computations

In this paper we provide a simple characterization of (weak) fairness of components as defined by Costa and Stirling in [Weak and strong fairness in CCS, Inform. and Comput. 73 (1987) 207–244]. The study is carried out at system specification level by resorting to a common process description language. This paper follows and exploits similar techniques as those developed in [F. Corradini, M.R. Di Berardini, W. Vogler, Relating fairness and timing in process algebras, Proc. of Concur’03, Lecture Notes in Computer Science, Vol. 2761, Springer, Berlin, 2003, pp. 446–460]—where fairness of actions was taken into account and was contrasted to the PAFAS timed operational semantics—but the characterization of fair executions is based on a new semantics for PAFAS; it makes use of only two copies of each basic action instead of infinitely many as in [G. Costa, C. Stirling, Weak and strong fairness in CCS, Inform. and Comput. 73 (1987) 207–244] and allows for a simple and finite representation of fair executions by using regular expressions.The new semantics can also be understood as describing timed behaviour of systems with upper time bounds. The paper discusses in detail how this new semantics differs from the old one, and why theses changes are necessary to properly capture fairness of components.