Priority as Extremal Probability
S. A. Smolka, B. Steffen
We extend the stratified model of probabilistic processes
presented in [GSST90] to obtain a very general notion of
process priority. The main idea is to allow probability
guards of value 0 to be associated with alternatives of a
probabilistic summation expression. Such alternatives can
be chosen only if the non-zero alternatives are precluded
by contextual constraints. We refer to this model as
one of ``extremal probability'' and to its signature as
$\PCCSz$, where the \zeta signifies the possibility of
zero-probability alternatives. We provide PCCS_zeta with a
structured operational semantics and a notion of probabilistic
bisimulation, which is shown to be a congruence.
Of particular interest is the abstraction PCCS_pi of
PCCS_zeta in
which all non-zero probability guards are identified. Both the
operational and bisimulation semantics of PCCS_zeta easily
adapt to this abstraction. PCCS_pi represents a customized
framework for reasoning about priority, and covers all features
of process algebras proposed for reasoning about priority that
we know of. This is illustrated by specifying a controller with
a dynamic priority structure for the readers-writers problem.