Parameter Synthesis Algorithms for Parametric Interval Markov Chains

  title={Parameter Synthesis Algorithms for Parametric Interval Markov Chains},
  author={Laure Petrucci and Jaco van de Pol},
This paper considers the consistency problem for Parametric Interval Markov Chains. In particular, we introduce a co-inductive definition of consistency, which improves and simplifies previous inductive definitions considerably. The equivalence of the inductive and co-inductive definitions has been formally proved in the interactive theorem prover PVS. 
Quantitative Analysis of Interval Markov Chains
This work compares three semantic interpretations proposed in the literature in the context of model-checking rPCTL, an extension of PCTL where each path-formula is equipped with the specification of a bound on the accumulated reward.
Parameter Synthesis for Markov Models
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Parametric Verification: An Introduction
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Reasoning on Stochastic Models in Systems Biology Under Uncertainty
  • Krishnendu Ghosh
  • Computer Science
    2020 IEEE 20th International Conference on Bioinformatics and Bioengineering (BIBE)
  • 2020
This work creates a formalism that is based on interval Markov chains with open intervals to address uncertainty in the environment and an automated abstraction of the intervals Markov chain based model is described.
Interval Markov Decision Processes with Multiple Objectives
This article considers Interval Markov decision processes (IMDPs), which generalise classical MDPs by having interval-valued transition probabilities, and investigates the problem of robust multi-objective synthesis for IMDPs and Pareto curve analysis of multi- objective queries on IM DPs and shows that the multi-Objective synthesis problem is PSPACE-hard.


Consistency for Parametric Interval Markov Chains
This paper investigates the consistency problem for Interval Markov Chains with parametric intervals and proposes an efficient solution for the subclass of parametric IMCs with local parameters only, and shows that this problem is still decidable for parametricIMCs with global parameters, although more complex in this case.
Parameter Synthesis for Parametric Interval Markov Chains
Interval Markov Chains IMCs are the base of a classic probabilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In
New results for Constraint Markov Chains
Parameter Synthesis for Markov Models: Faster Than Ever
The technique provides the first sound and feasible method for performing parameter synthesis of Markov decision processes and outperforms the existing analysis of parametric Markov chains by several orders of magnitude regarding both run-time and scalability.
Model Checking of Open Interval Markov Chains
It is shown that, as far as model checking (and reachability) is concerned, open intervals does not cause any problem, and with minor modification existing algorithms can be used for model checking interval Markov chains against PCTL formulas.
Symbolic and Parametric Model Checking of Discrete-Time Markov Chains
A language-theoretic approach to symbolic model checking of PCTL over discrete-time Markov chains, which allows for parametric model checking by evaluating the regular expression for different parameter values, to study the influence of a lossy channel in the overall reliability of a randomized protocol.
Parametric probabilistic transition systems for system design and analysis
We develop a model of parametric probabilistic transition Systems (PPTSs), where probabilities associated with transitions may be parameters. We show how to find instances of the parameters that
Reachability in Parametric Interval Markov Chains Using Constraints
This work investigates the difference between pIMCs and other Markov Chain abstractions models and investigates the two usual semantics for IMCs, and proves that both semantics agree on the maximal/minimal reachability probabilities of a given IMC.
Probabilistic Reachability for Parametric Markov Models
It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (n *** (logn )), so a new approach is needed to arrive at an effective method that avoids this blow up in most practical cases.
On the complexity of model checking interval-valued discrete time Markov chains