# 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}
}
• Published in CAV 15 July 2000
• Computer Science
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…
195 Citations

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## References

SHOWING 1-10 OF 47 REFERENCES

### Approximate Symbolic Model Checking of Continuous-Time Markov Chains

• Mathematics, Computer Science
CONCUR
• 1999
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

• Computer Science
ICALP
• 2000
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

• Mathematics
TACAS
• 2000
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

• Computer Science, Mathematics
CAV
• 1995
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

• Computer Science
[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
• 1988
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

### Verifying Continuous Time Markov Chains

• Mathematics, Computer Science
CAV
• 1996
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

• Mathematics
Oper. Res.
• 1984
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.