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.