Summary: Local Liveness
for Compositional Modeling of Fair Reactive Systems ?
Rajeev Alur 1 and Thomas A. Henzinger 2??
1 AT&T Bell Laboratories, Murray Hill, NJ
2 Department of Computer Science, Cornell University, Ithaca, NY
Abstract. We argue that the standard constraints on liveness condi
tions in nonblocking trace models---machine closure for closed systems,
and receptiveness for open systems---are unnecessarily weak and com
plex, and that liveness should, instead, be specified by augmenting transi
tion systems with acceptance conditions that satisfy a locality constraint.
First, locality implies machine closure and receptiveness, and thus per
mits the composition and modular verification of live transition systems.
Second, while machine closure and receptiveness are based on infinite
games, locality is based on repeated finite games, and thus easier to
check. Third, no expressive power is lost by the restriction to local live
ness conditions. We illustrate the appeal of local liveness using the model
of Fair Reactive Systems, a nonblocking trace model of communicating
In the hierarchical development of systems, the designer models a system at dif