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Model-Checking Algorithms for Continuous-Time Markov Chains
- C. Baier, B. Haverkort, H. Hermanns, J. Katoen
- Computer ScienceIEEE Trans. Software Eng.
- 1 April 2002
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.
Interactive Markov Chains
- H. Hermanns
- Computer ScienceLecture Notes in Computer Science
This paper presents a meta-analyses of interactive Markov Chains and its applications to knowledge representation, specifically in the context of knowledge representation and representation in the discrete-time model.
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 Probabilistic Automata in Continuous Time
- Christian Eisentraut, H. Hermanns, Lijun Zhang
- Mathematics, Computer Science25th Annual IEEE Symposium on Logic in Computer…
- 11 July 2010
We develop a compositional behavioural model that integrates a variation of probabilistic automata into a conservative extension of interactive Markov chains. The model is rich enough to embody the…
Discrete-Time Rewards Model-Checked
The temporal logic probabilistic CTL is extended with reward constraints and formulae to formulate complex measures – involving expected as well as accumulated rewards – in a precise and succinct way are introduced.
The Ins and Outs of the Probabilistic Model Checker MRMC
- J. Katoen, Ivan S. Zapreev, E. M. Hahn, H. Hermanns, D. Jansen
- Computer ScienceSixth International Conference on the…
- 1 February 2011
The Markov Reward Model Checker (MRMC) is a software toolfor verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their rewardextensions. Distinguishing…
Weak Bisimulation for Fully Probabilistic Processes
This paper gives an algorithm to decide weak (and branching) bisimulation with a time complexity cubic in the number of states of the fully probabilistic system, and illustrates that due to these properties, weak bisimulations provides all the crucial ingredients for mechanised compositional veri�cation of Probabilistic transition systems.
Probabilistic Termination: Soundness, Completeness, and Compositionality
A framework to prove almost sure termination for probabilistic programs with real valued variables, based on ranking supermartingales, which is proven sound and complete for a meaningful class of programs involving randomization and bounded nondeterminism.
This paper explores foundational questions of CEGAR in the context of predicate abstraction in the area of automatic verification of probabilistic systems.
Comparative branching-time semantics for Markov chains
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…