Related papers: Rate Reduction for State-labelled Markov Chains wi…
In this paper, we consider a general class of two-time-scale Markov chains whose transition rate matrix depends on a parameter $\lambda>0$. We assume that some transition rates of the Markov chain will tend to infinity as…
We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…
This paper focuses on the design of time-invariant memoryless control policies for fully observed controlled Markov chains, with a finite state space. Safety constraints are imposed through a pre-selected set of forbidden states. A state is…
In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces,…
In the design of probabilistic timed systems, bounded requirements concerning behaviour that occurs within a given time, energy, or more generally cost budget are of central importance. Traditionally, such requirements have been…
Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…
Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…
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…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
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…
A continuous-time Markov chain (CTMC) execution is a continuous class of probability distributions over states. This paper proposes a probabilistic linear-time temporal logic, namely continuous-time linear logic (CLL), to reason about the…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical…
Markov Chains with variable length are useful stochastic models for data compression that avoid the curse of dimensionality faced by that full Markov Chains. In this paper we introduce a Variable Length Markov Chain whose transition…
We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…