Modelling Asynchrony with a Synchronous Model

The I/O Automaton paradigm of Lynch and Tuttle models asynchrony through an in-terleaving parallel composition and generalizes more common interleaving models based upon message-passing, such as Hoare's CSP. It is not generally recognized that such inter-leaving models in fact can be viewed as special cases of synchronous parallel composition, in which components all move in lock-step. Let A be any set of nite-state I/O Automata drawing actions from a xed nite set containing a subset. In this article we establish a translation T : A ! P to a class of !-automata P closed under a synchronous parallel composition , for which T is monotonic with respect to implementation relative to , and linear A and A = A 1 jj jjA m , B = B 1 jj jjB n , if is the set of actions common to both A and B, then A implements B (in the sense of I/O Automata) if and only if the !-automaton language containment L(T(A 1) T(A m)) L(T(B 1) T(B n)) obtains, where jj denotes the interleaving parallel composition on A and denotes the synchronous parallel composition on P. For the class P, we use the L-process model of !-automata. This result enables one to verify systems speciied by I/O Automata through model-checkers such as COSPAN or SMV, that operate on models with synchronous parallel composition. The translation technique generalizes to other interleaving models, although in each case, the translation map must match the speciic model.