Model Checking Continuous-Time Markov Chains by Transient Analysis

@inproceedings{Baier2000ModelCC,
  title={Model Checking Continuous-Time Markov Chains by Transient Analysis},
  author={Christel Baier and Boudewijn R. Haverkort and Holger Hermanns and Joost-Pieter Katoen},
  booktitle={CAV},
  year={2000}
}
The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3,6], a stochastic branching-time temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form \({\cal P}_{\bowtie p}(\Phi_1 \, {\cal U}^{I} \, \Phi_2)\), for state formulas Φ1 and Φ2, comparison operator ⋈, probability p, and real interval I. The main result of this paper is that… 

Model-Checking Algorithms for Continuous-Time Markov Chains

TLDR
The problem of model-checking time-bounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs and a variant of lumping equivalence (bisimulation) preserves the validity of all formulas in the logic.

Model Checking of Continuous-Time Markov Chains by Closed-Form Bounding Distributions

TLDR
This paper proposes to apply stochastic comparison technique to construct bounding models having a special structure which provides closed- form solutions to compute both transient and steady-state distributions and presents an algorithm to provide rapid model checking by means of these closed-form bounding distributions.

Model Checking CSL until Formulae with Random Time Bounds

TLDR
The efficient model checking of CTMCs against the logic CSL developed in [13] is extended to cater for a random time-bounded until operator, where the time bound is given by a random variable instead of a fixed real-valued time (or interval).

Central Limit Model Checking

TLDR
A continuous-space approximation of the CTMC in terms of a Gaussian process based on the Central Limit Approximation, whose solution requires solving a number of differential equations that is quadratic in the number of species and independent of the population size is employed.

Finite-state abstractions for probabilistic computation tree logic

Probabilistic Computation Tree Logic (PCTL) is the established temporal logic for probabilistic verification of discrete-time Markov chains. Probabilistic model checking is a technique that verifies

Performance and reliability model checking and model construction

TLDR
This talk introduces continuous-time Markov chains and discusses the use of model checking to assess performance and reliability properties of CTMCs, and focuses on high-level formalisms supporting a modern, hierarchical and compositional design methodology.

Model checking Markov chains : techniques and tools

TLDR
This dissertation introduces MRMC, a model checker for DMRMs and CMRMs, that supports reward extensions of PCTL and CSL, and deriving techniques based on discrete-event sijulation and sequential confidence intervals for model checking CSL properties on CTMCs.

Efficient CSL Model Checking Using Stratification

TLDR
A measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one is presented, making the present work the centerpiece of a broadly applicable full CSL model checker.

Safety Verification of Continuous-Space Pure Jump Markov Processes

TLDR
A formal method to abstract the process as a finite-state discrete-time Markov chain is described, which provides a-priori error bounds on the precision of the abstraction, based on the continuity properties of the stochastic kernel of the process and of its jump rate function.

Comparative branching-time semantics for Markov chains

...

References

SHOWING 1-10 OF 47 REFERENCES

Approximate Symbolic Model Checking of Continuous-Time Markov Chains

TLDR
A symbolic approximate method for solving the integrals using MTDDs (multi-terminal decision diagrams), a generalisation of MTBDDs, suitable for numerical integration using quadrature formulas based on equally-spaced abscissas, like trapezoidal, Simpson and Romberg integration schemes.

On the Logical Characterisation of Performability Properties

TLDR
It is argued that this logic is adequate for expressing performability measures of a large variety and implies that reward-based properties expressed in CRL for a particular Markov reward model can be interpreted as CSL properties over a derived continuous-time Markov chain, so that model checking procedures for CSL can be employed.

A Markov Chain Model Checker

TLDR
A prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker (E ⊢ MC2), where properties are expressed in appropriate extensions of CTL, is described.

It Usually Works: The Temporal Logic of Stochastic Systems

TLDR
The universe of models is extended to generalized Markov processes in order to support notions of refinement, abstraction, and parametrization and model checking pCTL* over generalized MarkOV processes is shown to be elementary by a reduction to RCF.

Verifying temporal properties of finite-state probabilistic programs

The complexity of testing whether a finite-state (sequential or concurrent) probabilistic program satisfies its specification expressed in linear temporal logic. For sequential programs an

Process algebra for performance evaluation

Automated compositional Markov chain generation for a plain-old telephone system

Characterizing Finite Kripke Structures in Propositional Temporal Logic

Verifying Continuous Time Markov Chains

TLDR
The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number theory.

The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes

TLDR
An implementation for a general class of Markov processes that can be described in terms of state space S, event set E, rate vectors R, and target vectors T-abbreviated as SERT is presented.