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.... Simple example and possible PRISM representations “what is the expected number of complexation reactions before relocation occurs?”. For further details on probabilistic model checking of CTMCs see =-=[16]-=-. PRISM [5,6] is a probabilistic checking tool developed at the University of Birmingham. Models are specified in a simple state-based language based on Reactive Modules. An extension of the temporal ...

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...cisely, the expected value of a random variable, associated with particular reward structure). For a presentation of the formal semantics of the PRISM property specification language, see for example =-=[13]-=-. In the remainder of this section, we give an overview of the different types of property that are available and examples of the kinds of performability measures that they can be used to express. Tra...

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...s probabilistic model checking algorithms and their implementation, and gives an illustration of the application of these techniques to some large case studies. The tutorial is intended to complement =-=[67]-=-, which focuses on probabilistic model checking for discrete- and continuous-time Markov chains, rather than Markov decision processes. There is also an accompanying website [91], providing models for...

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... determine the probabilities Probs(Φ U ≤k Ψ) for all states s where k ∈ N ∪ {∞}. When k ∈ N, the corresponding vector Prob(Φ U ≤k Ψ) can be expressed in terms of the transient probabilities of a DTMC =-=[24]-=-. Firstly, for any DTMC D = (S, s, P, L) and PCTL formula Φ, let D[Φ] = (S, s, P[Φ], L) be the DTMC D modified as follows: if s �|= Φ, then P[Φ](s, s ′ ) = P(s, s ′ ) for all s ′ ∈ S, and if s |= Φ, t...

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...itional investigations will also relate PCCP to other semantic approaches towards probabilistic computation, e.g. probabilistic predicate transformers [18, 16], probabilistic logic and model checking =-=[2, 10], and prob-=-abilistic process algebras [3]. A possible extension of the PCCP language can be obtained by considering a "fuzzy" constraint system where strict entailment is replaced by a weighted justifi...

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...t holds that Pr Du (s0,B) = f[V/u]. Parametric MRMs. Let R = (D,r) be a PMRM with D = (S,s0,P,V ). Let B ⊆ S be a set of target states. We are interested in the parametric expected accumulated reward =-=[18]-=- until B, which is denoted by R(s0,B). Formally, R(s0,B) is the expectation of the random variable X : σ ∈ Path D (s0) → R≥0 which is defined by: X(σ) equals 0 if first(σ) ∈ B, ∞ if σ[i] /∈ B for all ...

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...ut, by employing formal verification techniques, compute exact quantitative measures as opposed to taking averages over sets of simulation runs. In this paper we show how probabilistic model checking =-=[2, 21, 31]-=- and the probabilistic model checker PRISM [15, 26] can be employed as a framework for the modelling and analysis of biological pathways. This approach is motivated by both the fact that PRISM has alr...

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...n, such as efficient and numerically robust methods for the computation of transient and steady-state probability distributions [1], [2], fast simulation algorithms [3], and stochastic model checking =-=[4]-=-. However, as with most discrete-state analysis techniques, the major drawback is the well-known problem of state-space explosion (i.e., the number of reachable states of the chain grows combinatorial...