The How and Why of Interactive Markov Chains

Hermanns, Holger; Katoen, Joost-Pieter

doi:10.1007/978-3-642-17071-3_16

Cited by 33 publications

(34 citation statements)

References 61 publications

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“…A FuTS S is called total and deterministic if for each transition relation i ⊆ S × L i × FS(S , R i ) involved and for all s ∈ S , ∈ L i , we have s i v for exactly one v ∈ FS(S , R i ). In such a situation, the In Section 6 we will provide semantics for the process language IML of interactive Markov chains [13,16] using FuTS. Unlike many other stochastic process algebras, a single IML process can in general both perform action-based transitions and time-delays governed by exponential distributions.…”

Section: Labeled State-to-function Transition Systemsmentioning

confidence: 99%

Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Latella

Massink

Vink

2012

Electron. Proc. Theor. Comput. Sci.

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Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with stochastic process languages. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is proven stating that FuTS-bisimulation coincides with the behavioral equivalence of the associated functor. As generic examples, the concrete existing equivalences for the core of the stochastic process algebras PEPA and IML are related to the bisimulation of specific FuTS, providing via the correspondence result coalgebraic justification of the equivalences of these calculi.

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Section: Labeled State-to-function Transition Systemsmentioning

confidence: 99%

Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Latella

Massink

Vink

2012

Electron. Proc. Theor. Comput. Sci.

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“…LTSs (labeled transition systems) are one of the main operational models for concurrency and are equipped with a plethora of behavioral equivalences like bisimulation and trace equivalences. A natural mixture of CTMCs and LTSs yields so-called interactive Markov chains (IMCs), originally proposed as a semantic model of stochastic process algebras [19,20]. As a state may have several outgoing actiontransitions, IMCs are in fact stochastic real-time 1 1 2 -player games, also called continuous-time probabilistic automata by Knast in the 1960's [22].…”

Section: Introductionmentioning

confidence: 99%

Quantitative Timed Analysis of Interactive Markov Chains

Guck

Han

Katoen

et al. 2012

Lecture Notes in Computer Science

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Abstract. This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2 -player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering formalisms such as AADL and dynamic fault trees. We provide algorithms for determining the extremal expected time of reaching a set of states, and the long-run average of time spent in a set of states. The prototypical tool Imca supports these algorithms as well as the synthesis of ε-optimal piecewise constant timed policies for timed reachability objectives. Two case studies show the feasibility and scalability of the algorithms.

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“…The key feature of Interactive Markov Chains (IMCs) [Hermanns 2002;Hermanns and Katoen 2010] We could use simple FuTSs for IMCs, by just considering as co-domain of continuations a semi-ring of the form R ≥0 ∪ {∞}, where classical operations on reals are extended as follows: ∀x 0 : x·∞ = ∞, 0·∞ = 0 and ∀x.x+∞ = ∞. Elements in R >0 would indicate rates of Markovian transitions (with 0 denoting un-reachability, as usual), while ∞ would characterize interactive ones, following the intuition that the latter, being immediate, have an infinite rate.…”

Section: A Language For Interactive Markov Chainsmentioning

confidence: 99%

A uniform definition of stochastic process calculi

et al. 2013

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We introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state-transition structures where each transition is a triple of the form (s, α, P). The first and the second components are the source state, s, and the label, α, of the transition, while the third component is the continuation function, P, associating a value of a suitable type to each state s . For example, in the case of stochastic process algebras the value of the continuation function on s represents the rate of the negative exponential distribution characterizing the duration/delay of the action performed to reach state s from s. We first provide the semantics of a simple formalism used to describe Continuous-Time Markov Chains, then we model a number of process algebras that permit parallel composition of models according to the two main interaction paradigms (multiparty and one-to-one synchronization). Finally, we deal with formalisms where actions and rates are kept separate and address the issues related to the co-existence of stochastic, probabilistic, and non-deterministic behaviors. For each formalism, we establish the formal correspondence between the FuTSs semantics and its original semantics.

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The How and Why of Interactive Markov Chains

Cited by 33 publications

References 61 publications

Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Quantitative Timed Analysis of Interactive Markov Chains

A uniform definition of stochastic process calculi

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