Task-Structured Probabilistic I/O Automata

Abstract

Modeling frameworks such as Probabilistic I/O Automata (PIOA) andMarkov Decision Processes permit both probabilistic andnondeterministic choices. In order to use such frameworks to express claims about probabilities of events, one needs mechanisms for resolving nondeterministic choices. For PIOAs, nondeterministic choices have traditionally been resolved by schedulers that have perfect information about the past execution. However, such schedulers are too powerful for certain settings, such as cryptographic protocol analysis, where information must sometimes be hidden. Here, we propose a new, less powerful nondeterminism-resolutionmechanism for PIOAs, consisting of tasks and local schedulers.Tasks are equivalence classes of system actions that are scheduled byoblivious, global task sequences. Local schedulers resolve nondeterminism within system components, based on local information only. The resulting task-PIOA framework yields simple notions of external behavior and implementation, and supports simple compositionality results.We also define a new kind of simulation relation, and show it to besound for proving implementation. We illustrate the potential of the task-PIOA framework by outlining its use in verifying an Oblivious Transfer protocol.