Partial order reduction on concurrent probabilistic programs

On Model Checking Techniques for Randomized Distributed Systems

“…In the context of partial order reduction for MDPs, it has been noticed in [4,14] that the criteria that are known to be sound for non-probabilistic systems are not sufficient to preserve extremal probabilities for ω-regular path events. In this setting, the problem is that the commutativity of independent probabilistic actions is a local property that does not carry over to a global setting.…”

“…-For the schedulers that first choose one of the actions β or γ and then perform α, an outcome where x = y ∈ {1, 2} hold is obtained with probability 1 2 . This observation causes some care for the design of partial order reduction techniques for MDPs and either requires an extra condition [4,14] or to restrict the class of schedulers for the worst-case analysis [17].…”

Confluence reduction for Markov automata

“…Confluence reduction for process algebras was first introduced for non-probabilistic systems [7], and later for probabilistic automata [25]. Also, several types of partial order reduction (POR) have been defined, both for nonprobabilistic [26,21,16] and probabilistic systems [11,4,3]. These techniques are based on ideas similar to confluence, and have been compared to confluence recently, both in a theoretical [17] and in a practical manner [18].…”

Confluence Reduction for Markov Automata

“…Confluence reduction for process algebras was first introduced for non-probabilistic systems [7], and later for probabilistic automata [25]. Also, several types of partial order reduction (POR) have been defined, both for nonprobabilistic [26,21,16] and probabilistic systems [11,4,3]. These techniques are based on ideas similar to confluence, and have been compared to confluence recently, both in a theoretical [17] and in a practical manner [18].…”