Strategic Dominance: A New Preorder for Nondeterministic Processes

Abstract: We study the following refinement relation between nondeterministic state-transition models: model B strategically dominates model A iff every deterministic refinement of A is language contained in some deterministic refinement of B. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between A and B: every strategy that resolves the nondeterminism of A is dominated by a strategy that resolves the nondeterminism of B. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.