Related papers: Approximate Probabilistic Bisimulation for Continu…

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…

In this work, we generalize the concept of bisimulation metric in order to metrize the behaviour of continuous-time processes. Similarly to what is done for discrete-time systems, we follow two approaches and show that they coincide: as a…

A new weak bisimulation semantics is defined for Markov automata that, in addition to abstracting from internal actions, sums up the expected values of consecutive exponentially distributed delays possibly intertwined with internal actions.…

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…

This paper presents algorithms for identifying and reducing a dedicated set of controllable transition rates of a state-labelled continuous-time Markov chain model. The purpose of the reduction is to make states to satisfy a given…

This paper develops a decision algorithm for weak bisimulation on Markov Automata (MA). For that purpose, different notions of vanishing state (a concept known from the area of Generalised Stochastic Petri Nets) are defined. Vanishing…

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…

The bisimulation metric (BSM) is a powerful tool for analyzing state similarities within a Markov decision process (MDP), revealing that states closer in BSM have more similar optimal value functions. While BSM has been successfully…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

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…

Behavioural distances generally offer more fine-grained means of comparing quantitative systems than two-valued behavioural equivalences. They often relate to quantitative modalities, which generate quantitative modal logics that…

We introduce a formal notion of masking fault-tolerance between probabilistic transition systems based on a variant of probabilistic bisimulation (named masking simulation). We also provide the corresponding probabilistic game…

We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…

We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of…

Bisimulation is a concept that captures behavioural equivalence of states in a variety of types of transition systems. It has been widely studied in discrete-time settings where a key notion is the bisimulation metric which quantifies "how…

We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…

Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…

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…

This note presents conjectures on polynomial/algebraic/sub-exponential convergence of transition probabilities for $\lambda$-null recurrent and $\lambda$-transient Markov chains in continuous time. The only known positive examples are in…

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…