# 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…

## 195 Citations

### Model-Checking Algorithms for Continuous-Time Markov Chains

- Computer ScienceIEEE Trans. Software Eng.
- 2003

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

- Computer ScienceThird International Conference on the Quantitative Evaluation of Systems - (QEST'06)
- 2006

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

- Mathematics, Computer SciencePAPM-PROBMIV
- 2002

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

- Computer Science, MathematicsACM Trans. Comput. Log.
- 2019

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

- Computer Science
- 2011

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

- Computer Science
- 2000

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

- Computer Science
- 2008

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

- Computer Science, Mathematics
- 2011

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

- Mathematics, Computer ScienceTACAS
- 2016

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.

## References

SHOWING 1-10 OF 47 REFERENCES

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

- Mathematics, Computer ScienceCONCUR
- 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 ScienceICALP
- 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

- MathematicsTACAS
- 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, MathematicsCAV
- 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…

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

- Computer Science, MathematicsSci. Comput. Program.
- 2000

### Characterizing Finite Kripke Structures in Propositional Temporal Logic

- MathematicsTheor. Comput. Sci.
- 1988

### Verifying Continuous Time Markov Chains

- Mathematics, Computer ScienceCAV
- 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

- MathematicsOper. 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.