Summary: Deriving Complete Inference Systems for a Class of GSOS
Languages Generating Regular Behaviours
Luca Aceto \Lambda
School of Cognitive and Computing Studies,
University of Sussex,
Falmer, Brighton BN1 9QH, England
Many process algebras are defined by structural operational semantics (SOS). Indeed, most
such definitions are nicely structured and fit the GSOS format of . In  B. Bloom, F.
Vaandrager and I presented a procedure for converting any GSOS language definition to a finite
complete equational axiom system which precisely characterizes strong bisimulation of processes.
For recursion theoretic reasons, such a complete equational axiom system included, in general,
one infinitary induction principle --- essentially a reformulation of the Approximation Induction
Principle (AIP) [7, 6].
However, it is wellknown that AIP and other infinitary proof rules are not necessary for
the axiomatization of, e.g., strong bisimulation over regular behaviours (see [29, 8, 31]). In
this paper, following , I characterize a class of infinitary GSOS specifications, obtained by
relaxing some of the finiteness constraints of the original format of Bloom, Istrail and Meyer,
which generate regular processes. I then show how the techniques of  can be adapted to give a