Model Checking Continuous-Time Markov Chains by Transient Analysis

  title={Model Checking Continuous-Time Markov Chains by Transient Analysis},
  author={Christel Baier and Boudewijn R. Haverkort and Holger Hermanns and Joost-Pieter Katoen},
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

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

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

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

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

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

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

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

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




Approximate Symbolic Model Checking of Continuous-Time Markov Chains

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

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

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

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

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

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.