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Syntax Throughout this monograph, we provide the definition of the syntax of logics in a more relaxed way. Skipping the syntactic rules for brackets (which can be derived from the precedence order of the operators that will be declared in words), the above inductive definition of propositional formulae over AP can be rewritten as Φ ::= true ∣∣∣ a ∣∣∣ Φ1 ∧Φ2… (More)

- Christel Baier, Boudewijn R. Haverkort, Holger Hermanns, Joost-Pieter Katoen
- IEEE Trans. Software Eng.
- 2003

Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents… (More)

- Christel Baier, Joost-Pieter Katoen, Holger Hermanns
- CONCUR
- 1999

This paper presents a symbolic model checking algorithm for continuous-time Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al 1]. The considered logic contains a time-bounded until-operator and a novel operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system… (More)

This short tool paper introduces MRMC, a model checker for discrete-time and continuous-time Markov reward models. It supports reward extensions of PCTL and CSL, and allows for the automated verification of properties concerning long-run and instantaneous rewards as well as cumulative rewards. In particular, it supports to check the reachability of a set of… (More)

The verification of continuous-time Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steady-state properties and the specification of probabilistic timing properties of the form P⊲⊳p(Φ1 U I Φ2), for state formulas Φ1 and Φ2,… (More)

- Suzana Andova, Holger Hermanns, Joost-Pieter Katoen
- FORMATS
- 2003

This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and succinct way. Algorithms to efficiently analyze such… (More)

- Joost-Pieter Katoen, Ivan S. Zapreev, Ernst Moritz Hahn, Holger Hermanns, David N. Jansen
- Perform. Eval.
- 2009

The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions. Distinguishing features of MRMC are its support for computing timeand reward-bounded reachability probabilities, (property-driven) bisimulation minimization, and precise… (More)

Among other domains, learning finite-state machines is important for obtaining a model of a system under development, so that powerful formal methods such as model checking can be applied. A prominent algorithm for learning such devices was developed by Angluin. We have implemented this algorithm in a straightforward way to gain further insights to… (More)

- Christel Baier, Joost-Pieter Katoen, Holger Hermanns, Verena Wolf
- Inf. Comput.
- 2005

This paper presents various semantics in the branching-time spectrum of discrete-time and continuous-time Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation pre-orders are covered and are logically characterised in terms of the temporal logics PCTL and CSL. Apart from presenting various existing branching-time relations… (More)

- Christel Baier, Holger Hermanns, Joost-Pieter Katoen, Boudewijn R. Haverkort
- Theor. Comput. Sci.
- 2004

A continuous-time Markov decision process (CTMDP) is a generalization of a continuous-time Markov chain in which both probabilistic and nondeterministic choices co-exist. This paper presents an efficient algorithm to compute the maximum (or minimum) probability to reach a set of goal states within a given time bound in a uniform CTMDP, i.e., a CTMDP in… (More)