scholarly journals On the algebraic structure of certain partially observable finite-state Markov processes

1978 ◽  
Vol 38 (2) ◽  
pp. 179-212 ◽  
Author(s):  
Alan S. Willsky
Keyword(s):  
Markov Processes ◽  
Algebraic Structure ◽  
Finite State ◽  
Partially Observable

scholarly journals Inductive Synthesis for Probabilistic Programs Reaches New Horizons

2021 ◽  
pp. 191-209
Author(s):  
Roman Andriushchenko ◽  
Milan Češka ◽  
Sebastian Junges ◽  
Joost-Pieter Katoen
Keyword(s):  
Deductive Reasoning ◽  
Synthesis Process ◽  
Worst Case ◽  
New Horizons ◽  
The Family ◽  
Pruning Strategy ◽  
Finite State ◽  
Novel Method ◽  
Partially Observable ◽  
Probabilistic Programs

AbstractThis paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a reachability specification. The method builds on a novel inductive oracle that greedily generates counter-examples (CEs) for violating programs and uses them to prune the family. These CEs leverage the semantics of the family in the form of bounds on its best- and worst-case behaviour provided by a deductive oracle using an MDP abstraction. The method further monitors the performance of the synthesis and adaptively switches between inductive and deductive reasoning. Our experiments demonstrate that the novel CE construction provides a significantly faster and more effective pruning strategy leading to an accelerated synthesis process on a wide range of benchmarks. For challenging problems, such as the synthesis of decentralized partially-observable controllers, we reduce the run-time from a day to minutes.

On aggregated Markov processes

1986 ◽  
Vol 23 (01) ◽  
pp. 208-214 ◽  
Author(s):  
Donald R. Fredkin ◽  
John A. Rice
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Underlying Process ◽  
Finite State

A finite-state Markov process is aggregated into several groups. What can be learned about the underlying process from the aggregated one? We provide some partial answers to this question.

scholarly journals On the limiting spectral density of random matrices filled with stochastic processes

2019 ◽  
Vol 27 (2) ◽  
pp. 89-105 ◽  
Author(s):  
Matthias Löwe ◽  
Kristina Schubert
Keyword(s):  
Stochastic Process ◽  
Spectral Density ◽  
Random Matrices ◽  
Markov Processes ◽  
Random Matrix ◽  
Matrix Theory ◽  
Gibbs Measures ◽  
State Spaces ◽  
The Matrix ◽  
Finite State

Abstract We discuss the limiting spectral density of real symmetric random matrices. In contrast to standard random matrix theory, the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic process. Under assumptions on this process which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the stochastic process. If the filling is in a certain way compatible with the symmetry condition on the matrix, the limiting law of the empirical eigenvalue distribution is the well-known semi-circle law. For other fillings we show that the semi-circle law cannot be the limiting spectral density.

Forwards and backwards models for finite-state Markov processes

1979 ◽  
Vol 11 (1) ◽  
pp. 118-133 ◽  
Author(s):  
B. D. O. Anderson ◽  
T. Kailath
Keyword(s):  
Markov Processes ◽  
Power Spectra ◽  
Finite State ◽  
Rational Power ◽  
State Models ◽  
Finite State Models

The construction and properties of reversible and dynamically reversible models for finite-state Markov processes are studied. Certain results on approximating processes with rational power spectra with dynamically reversible finite-state models are also obtained.

scholarly journals Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

2018 ◽  
Vol 28 (1) ◽  
pp. 013109 ◽  
Author(s):  
Joshua B. Ruebeck ◽  
Ryan G. James ◽  
John R. Mahoney ◽  
James P. Crutchfield
Keyword(s):  
Markov Processes ◽  
Finite State
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