A logic for the specification and proof of regular controllable processes of CCS

Summary

This work has been motivated by the following general problem: find logics for the specification and proof of programs, described by terms of some algebra with given congruence relation. This relation is supposed to define a satisfactory concept for the behavioural comparison of programs. We require these logics to be adequate with respect to the term language, in the sense that two programs, behaviourally equivalent satisfy the same formulas and conversely. The term language considered is the subset of controllable, regular terms of CCS, on a vocabulary of actions A, with observational congruence. A term is said to be controllable if it is congruent to some term without occurrence of τ. We obtain an adequate logic whose language of formulas is obtained from constants true, false and ¦Nil¦ by using operators ∨, ∧, fixpoint operators, + and a for a∈A; the latter can be considered as extensions of the operators + and a for a∈A of CCS. As a result, controllable CCS terms can be considered as formulas of this logic and the problem of program verification is reduced to the proof of the validity of a formula.