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Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is hindered by three factors: quadratic growth in the number of rates as the CTMC state space expands,…

Methodology · Statistics 2026-02-09 Filippo Monti , Xiang Ji , Marc A. Suchard

Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov…

Machine Learning · Computer Science 2020-04-23 Yu Wang , Nima Roohi , Matthew West , Mahesh Viswanathan , Geir E. Dullerud

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…

Probability · Mathematics 2018-10-11 Alexander Erreygers , Jasper De Bock

In this paper, we propose an approximating framework for analyzing parametric Markov models. Instead of computing complex rational functions encoding the reachability probability and the reward values of the parametric model, we exploit the…

Logic in Computer Science · Computer Science 2023-11-15 Ying Liu , Andrea Turrini , Moritz Hahn , Bai Xue , Lijun Zhang

The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for…

Logic in Computer Science · Computer Science 2018-04-06 Paul Gainer , Ernst Moritz Hahn , Sven Schewe

The Probabilistic Computational Tree Logic (PCTL) is the main specification formalism for discrete probabilistic systems modeled by Markov chains. Despite serious research attempts, the decidability of PCTL satisfiability and validity…

Logic in Computer Science · Computer Science 2025-05-01 Miroslav Chodil , Antonín Kučera

Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…

Logic in Computer Science · Computer Science 2026-05-14 Milan Češka , Sebastian Junges , Luko van der Maas , Filip Macák , Tim Quatmann

The Pairwise Markov Chain (PMC) is a probabilistic graphical model extending the well-known Hidden Markov Model. This model, although highly effective for many tasks, has been scarcely utilized for continuous value prediction. This is…

Machine Learning · Statistics 2025-08-12 Elie Azeraf

We study the complexity of reductions for weighted reachability in parametric Markov decision processes. That is, we say a state p is never worse than q if for all valuations of the polynomial indeterminates it is the case that the maximal…

Logic in Computer Science · Computer Science 2023-05-11 Kasper Engelen , Guillermo A. Pérez , Shrisha Rao

Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…

Probability · Mathematics 2017-06-22 Thomas Krak , Jasper De Bock , Arno Siebes

This paper considers large families of Markov chains (MCs) that are defined over a set of parameters with finite discrete domains. Such families occur in software product lines, planning under partial observability, and sketching of…

Logic in Computer Science · Computer Science 2019-03-27 Milan Ceska , Nils Jansen , Sebastian Junges , Joost-Pieter Katoen

Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…

Logic in Computer Science · Computer Science 2018-06-14 Sebastian Arming , Ezio Bartocci , Krishnendu Chatterjee , Joost-Pieter Katoen , Ana Sokolova

We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…

Formal Languages and Automata Theory · Computer Science 2019-06-13 Étienne André , Benoît Delahaye , Paulin Fournier

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…

Artificial Intelligence · Computer Science 2014-08-12 Mathias Niepert

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…

Artificial Intelligence · Computer Science 2012-06-29 Mathias Niepert

Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL) are often used to describe specifications of probabilistic properties for discrete time and continuous time, respectively. In PCTL and CSL, the possibility of…

Logic in Computer Science · Computer Science 2011-11-15 Takashi Tomita , Shigeki Hagihara , Naoki Yonezaki

A cost Markov chain is a Markov chain whose transitions are labelled with non-negative integer costs. A fundamental problem on this model, with applications in the verification of stochastic systems, is to compute information about the…

Formal Languages and Automata Theory · Computer Science 2016-01-19 Christoph Haase , Stefan Kiefer , Markus Lohrey

In this paper, we propose a new logic for expressing and reasoning about probabilistic hyperproperties. Hyperproperties characterize the relation between different independent executions of a system. Probabilistic hyperproperties express…

Logic in Computer Science · Computer Science 2018-04-06 Erika Abraham , Borzoo Bonakdarpour

Unambiguous automata are nondeterministic automata in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against \omega-regular specifications…

Logic in Computer Science · Computer Science 2023-04-10 Christel Baier , Stefan Kiefer , Joachim Klein , David Müller , James Worrell