Process Algebra with Language Matching

An axiom system ACP lm is presented as a variant of the process algebra ACP (Algebra of Communicating Processes). The acronym ACP lm stands for ACP with abstraction, extended with operators and axioms for language matching. Language matching is a technique based on trace information for labelling and cutting oo process terms that do not match some given trace (or set of traces). It is shown that in combination with the axioms for action alphabets interesting results are derivable, the most important of which is the Redundancy Theorem 3.3.6, which roughly states that if no trace labels occur in the expression @ H (p l k q), where p l is a labelled version of some process p, then it holds that @ H (p l k q) = @ H (p k q). It is shown that under certain natural conditions a similar result holds when abstraction is applied to p l and p, respectively. As an example the Concurrent Alternating Bit Protocol (CABP) is veriied. The CABP is a simple communication protocol, which can be recursively speciied over the signature of ACP , and it can be regarded as a slightly morèsophisticated' variant of the well-known Alternating Bit Protocol. The veriication is carried out using ACP with language matching, extended with the abstraction rule CFAR b , and the conditional alphabet axioms. The veriication is split in two parts so that it is`modular', and during the veriication some basic knowledge about the expected behaviour of the system is used, in order to eeectively apply language matching. Note: The example in this paper is a revised version of Wam92], which also appeared in the proceedings of the workshop on protocol veriication in Mierlo, The Netherlands, 1992.