Schedulers are no Prophets

Abstract

Several formalisms for concurrent computation have been proposed in recent years that incorporate means to express stochastic continuous-time dynamics and non-determinism. In this setting, some obscure phenomena are known to exist, related to the fact that schedulers may yield too pessimistic verification results, since current nondeterminism can surprisingly be resolved based on prophesying the timing of future random events. This paper provides a thorough investigation of the problem, and it presents a solution: Based on a novel semantics of stochastic automata, we identify the class of schedulers strictly unable to prophesy, and show a path towards verification algorithms with respect to that class. The latter uses an encoding into the model of stochastic timed automata under arbitrary schedulers, for which model checking tool support has recently become available.

A Hierarchy of Scheduler Classes for Stochastic Automata

“…This prophetic scheduling has already been observed in [9], where a "fix" in the form of the spent lifetimes semantics was proposed. Hartmanns et al [25] have shown that this not only still permits prophetic scheduling, but even admits divine scheduling, where a scheduler can change the future. The authors propose a complex non-prophetic semantics that provably removes all prophetic and divine behaviour.…”

“…The authors propose a complex non-prophetic semantics that provably removes all prophetic and divine behaviour. Much of the complication of the non-prophetic semantics of [25] is due to it being specified for open SA that include delayable actions. For the closed SA setting of this paper, prophetic scheduling can be more easily excluded by hiding from the schedulers all information about what will happen in the future of the system's evolution.…”

“…Understanding the capabilities of scheduler classes helps decide on the tradeoff between simplicity and the ability to attain optimal results. We use two perspectives on schedulers from the literature: the classic complete-information residual lifetimes semantics [9], where optimality is defined via history-dependent schedulers that see the entire current state, and non-prophetic schedulers [25] that cannot observe the timing of future events. Within each perspective, we define classes of schedulers whose views of the state and history are variously restricted (Sect.…”

Learning optimal decisions for stochastic hybrid systems

“…Furthermore, schedulers with knowledge on future random events, i.e. the sampled values, are called prophetic schedulers [23]. Schedulers without that knowledge are nonprophetic.…”

“…Hybrid Petri nets with general transitions (HPnGs) [19] form a restricted subclass of SHM [39] with linear dynamics. Their inherent nondeterminism was optimally resolved analytically in [38,42] via (non)prophetic [23] scheduling. The HPnG simulator HYPEG [37] has recently been extended to support linear and nonlinear differential equations in HPnG [36,40], but again cannot optimize over nondeterminism.…”