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 [G. Costa, C. Stirling. Weak and Strong Fairness in CCS. Information and Computation 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 and W. Vogler. Relating Fairness and Timing in Process Algebras. Proc. of Concur'03, Lect. Notes Comp. Sci. 2761, pp. 446-460, 2003] - 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. Information and Computation 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.