On Probabilistic Alternating Simulations

Zhang, Chenyi; Pang, Jun

doi:10.1007/978-3-642-15240-5_6

Cited by 13 publications

(12 citation statements)

References 20 publications

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“…To establish this, we show that, for every σ ∈ Σ, there exists σ ∈ Σ such that, for every π ∈ Π, there exists π ∈ Π such that Prob σ,π s (ϕ) = Prob σ ,π t (ϕ). The proof of this fact can be derived as a special case of Lemma 8 of [ZP10], which corresponds to a game-based version of the "execution correspondence theorem" of [Seg95]. Intuitively, the proof proceeds by showing that, for every σ ∈ Σ and π ∈ Π, there exist σ ∈ Σ and π ∈ Π such that the Markov chains obtained from strategy profile (σ, π) and from (σ , π ) are probabilistically bisimilar from their initial states s and t, respectively.…”

Section: Probabilistic Bisimulationmentioning

confidence: 97%

Verification and control for probabilistic hybrid automata with finite bisimulations

Sproston¹

2019

Journal of Logical and Algebraic Methods in Programming

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A hybrid automaton is a formal model for a system characterised by a combination of discrete and continuous components. Probabilistic hybrid automata generalise hybrid automata with the possibility of representing random behaviour of the discrete components of the system, in addition to nondeterministic choice regarding aspects such as time durations between mode switches and gradients of continuous flows. Two standard problems for probabilistic hybrid automata are verification and control: verification concerns the existence of a resolution of nondeterminism such that the resulting probability of an ω-regular property exceeds some bound; control concerns the existence of a resolution of the controllable nondeterminism, however the uncontrollable nondeterminism of the environment of the system is resolved, such that the probability of an ω-regular property exceeds some bound. While simple verification and control problems for (probabilistic) hybrid automata are in general undecidable, previous work has defined various subclasses for which the problems are decidable. In this paper, we generalise previous results by showing how bisimulation-based finite abstractions of non-probabilistic hybrid automata can be lifted to the setting of probabilistic hybrid automata. We apply these results to the subclass of probabilistic rectangular hybrid automata in a semantics in which discrete control transitions can occur only at integer points in time. These results allow us to show that, for this class of probabilistic hybrid automaton, the verification problems and control problems are decidable.

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Section: Probabilistic Bisimulationmentioning

confidence: 97%

Verification and control for probabilistic hybrid automata with finite bisimulations

Sproston¹

2019

Journal of Logical and Algebraic Methods in Programming

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“…Exact probabilistic (bi-)simulation relations via lifting. Similar to the alternating notions for probabilistic game structures in [38], we provide a simulation that relates any input chosen for the first process with one for the second process. As such, we allow for more elaborate handling of the inputs than in the probabilistic simulation relations discussed in [16,17], and further pave the way towards the inclusion of output maps.…”

Section: Lifting For General Markov Decision Processes Consider Two mentioning

confidence: 99%

Verification of General Markov Decision Processes by Approximate Similarity Relations and Policy Refinement

Haesaert

Soudjani

Abate

2017

SIAM J. Control Optim.

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Abstract. In this work we introduce new approximate similarity relations that are shown to be key for policy (or control) synthesis over general Markov decision processes. The models of interest are discrete-time Markov decision processes, endowed with uncountably-infinite state spaces and metric output (or observation) spaces. The new relations, underpinned by the use of metrics, allow in particular for a useful trade-off between deviations over probability distributions on states, and distances between model outputs. We show that the new probabilistic similarity relations, inspired by a notion of simulation developed for finite-state models, can be effectively employed over general Markov decision processes for verification purposes, and specifically for control refinement from abstract models.

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“…If s PA-I-simulates t and t PA-I-simulates s, we say s and t are PA-I-simulation equivalent. 6 PA-I-simulation has been shown to preserve a fragment of PATL which covers the ability of player I to enforce certain temporal requirements [30]. For example, if in state s player I can enforce reaching some states satisfying p within 5 transition steps and with probability at least 1 2 , written s |= I ≥ 1 2 ♦ ≤5 p, then for every state t that simulates s with respect to I, i.e., s t by some PA-Isimulation ' ', we also have t |= I ≥ 1 2 ♦ ≤5 p.…”

Section: Preliminariesmentioning

confidence: 99%

“…3 A probabilistic game structure (PGS) is a model that has probabilistic transitions, and allows the consideration of probabilistic choices of players. The simulation relation in PGSs, called probabilistic alternating simulation (PAsimulation), has been shown to preserve a fragment of probabilistic alternatingtime temporal logic (PATL) under mixed strategies, which is used in characterising what a group of players can enforce in such systems [30]. In this paper we propose a polynomial-time algorithm for computing the largest PA-simulation, which is, to the best of our knowledge, the first algorithm for computing a simulation relation in probabilistic concurrent games.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for Probabilistic Alternating Simulation

Zhang

Pang

2012

SOFSEM 2012: Theory and Practice of Computer Science

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In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation. It is to our knowledge the first such algorithm that works in polynomial time. Our solution extends the generalised coarsest partition problem (GCPP) to a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.

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On Probabilistic Alternating Simulations

Cited by 13 publications

References 20 publications

Verification and control for probabilistic hybrid automata with finite bisimulations

Verification and control for probabilistic hybrid automata with finite bisimulations

Verification of General Markov Decision Processes by Approximate Similarity Relations and Policy Refinement

An Algorithm for Probabilistic Alternating Simulation

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