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Consistency and refinement for Interval Markov Chains

Benoît Delahaye, Kim G. Larsen, Axel Legay, Mikkel L. Pedersen, Andrzej Wa¸sowski
2012 The Journal of Logic and Algebraic Programming  
Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18] .  ...  The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval constraints.  ...  Introduction Interval Markov Chains (IMCs for short) extend Markov Chains, by allowing to specify intervals of possible probabilities on state transitions.  ... 
doi:10.1016/j.jlap.2011.10.003 fatcat:finc3fhiqfcuxfcws5w5lqrksm

LTL Model Checking of Interval Markov Chains [chapter]

Michael Benedikt, Rastislav Lenhardt, James Worrell
2013 Lecture Notes in Computer Science  
Interval Markov chains (IMCs) generalize ordinary Markov chains by having interval-valued transition probabilities.  ...  We provide some analytical guarantees on the algorithm, and show how it can be combined with translation of logic to automata.  ...  Interval Markov Chains.  ... 
doi:10.1007/978-3-642-36742-7_3 fatcat:l3mhblxf3nfgrc7tssc2idw6eu

Decision Problems for Interval Markov Chains [chapter]

Benoît Delahaye, Kim G. Larsen, Axel Legay, Mikkel L. Pedersen, Andrzej Wąsowski
2011 Lecture Notes in Computer Science  
Interval Markov Chains (IMC) are the base of a classic probabilistic specification theory by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems.  ...  We also prove that deciding consistency of an IMC is polynomial and discuss suitable notions of determinism for such specifications.  ...  Introduction Interval Markov Chains (IMCs for short) extend Markov Chains, by allowing to specify intervals of possible probabilities on state transitions.  ... 
doi:10.1007/978-3-642-21254-3_21 fatcat:ccure3jcdrheth32k4t3v7t74y

Reachability in Augmented Interval Markov Chains [article]

Ventsislav Chonev
2017 arXiv   pre-print
In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend  ...  We study the qualitative, exact quantitative and approximate reachability problem, as well as natural subproblems thereof, and establish several upper and lower bounds for their complexity.  ...  Under the once-and-for-all interpretation, the given interval Markov chain is seen as representing an uncountably infinite collection of Markov chains refining it, and the goal is to determine whether  ... 
arXiv:1701.02996v1 fatcat:s2ffyncqwfcmzihxgfdv2xcvly

Compositional Design Methodology with Constraint Markov Chains

Benoit Caillaud, Benoit Delahaye, Kim G. Larsen, Axel Legay, Mikkel L. Pedersen, Andrzej Wasowski
2010 2010 Seventh International Conference on the Quantitative Evaluation of Systems  
We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC.  ...  Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs.  ...  ACKNOWLEDGEMENTS This work was supported by the European STREP-COMBEST project no. 215543, by VKR Centre of Excellence MT-LAB, and by an "Action de Recherche Collaborative" ARC (TP)I.  ... 
doi:10.1109/qest.2010.23 dblp:conf/qest/CaillaudDLLPW10 fatcat:mp7guy7ag5b37inwhxgaqewfsa

Quantitative Modal Transition Systems [chapter]

Kim G. Larsen, Axel Legay
2013 Lecture Notes in Computer Science  
This extended abstract offers a brief survey presentation of the specification formalism of modal transition systems and its recent extensions to the quantitative setting of timed as well as stochastic  ...  Implementation PA and specification APA of a coffee machine as Interval Markov Chains), where concrete probabilities are replaced with intervals, and with refinement providing a conservative extension  ...  ECDAR [25] gives an efficient tool support for refinement, consistency and quotienting for this theory.  ... 
doi:10.1007/978-3-642-37635-1_3 fatcat:tc6kcx2tcvcatminyfupo5sc3q

Orbits of turning points for maps of finite graphs and inverse limit spaces [article]

Brian Raines
2002 arXiv   pre-print
This leads to a new result regarding inverse limits of maps of the interval.  ...  This corollary extends Holte's theorem in the sense that the Markov partitions for f and g do not need to be the same set of points in the interval.  ...  Let each of f and g be Markov maps of the interval with associated Markov partitions, Theorem 4. 1 . 1 Let x ∈ lim ← {G, f } have the property that for some N ∈ N, if n ≥ N then deg(x n ) ∈ {0, 2}.  ... 
arXiv:math/0204137v1 fatcat:bnw3qzhssjabrong65mkqc7cpy

On scalable coding of hidden Markov sources

Mehdi Salehifar, Tejaswi Nanjundaswamy, Kenneth Rose
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
While several real world signals, such as speech, image and sensor network data, are modeled as hidden Markov sources (HMS) for recognition and analysis applications, their typical compression exploits  ...  At the enhancement layer, the state probability distribution is refined using available information from past enhancement layer reconstructed samples, and this refined estimate is further combined with  ...  Markov chains are common models for information sources with memory, and the memoryless channel is among the simplest communication models.  ... 
doi:10.1109/icassp.2016.7472433 dblp:conf/icassp/SalehifarNR16 fatcat:rzwzfxvjcfgi7dg4ialrqclfdi

Accompanying material for 'Lumpability for Uncertain Continuous-Time Markov Chains'

Luca Cardelli, Radu Grosu, Mirco Tribastone, Max Tschaikowski, Andrea Vandin
2019 Zenodo  
This is the accompanying material for the draft Luca Cardelli, Radu Grosu, Mirco Tribastone, Max Tschaikowski, and Andrea Vandin, Lumpability for Uncertain Continuous-time Markov Chains.  ...  The pdf is an extended version of the draft containing the proofs, while the archive contains information on how to replicate the experiments presented in the draft and all the used models.  ...  This work has been partially supported by the PRIN project "SEDUCE" no. 2017TWRCNB and by the FWF project "COCO" no. M 2393-N32.  ... 
doi:10.5281/zenodo.3478161 fatcat:4sd327alprgxnattgvykf6gf7a

Page 1896 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
The monograph consists of four chapters and an appendix. Chapter 1: Stochastic matrices and their variants. Chapter 2: Introduction to Markov set-chains. Chapter 3: Convergence of Markov set-chains.  ...  ISBN 3-540-64775-9 During the past twenty years the author has developed an interval mathematical technique for the investigation of nonhomogeneous Markov chains.  ... 

Computing invariant measures for expanding circle maps

Michael Keane, Rua Murray, Lai-Sang Young
1998 Nonlinearity  
We prove that a certain Markov approximation scheme based on a partition of S 1 into 2 N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous  ...  Markov chain on Z.  ...  The idea is to approximate the map globally by a Markov chain, and use the invariant probability measure for the Markov chain as an estimate of the physical invariant measure of the dynamical system.  ... 
doi:10.1088/0951-7715/11/1/004 fatcat:aiyfi555s5ey5gwyzba5rzn4xq

Organisation-Oriented Coarse Graining and Refinement of Stochastic Reaction Networks

Chunyan Mu, Peter Dittrich, David Parker, Jonathan E. Rowe
2018 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
We then construct and formalise a coarse-grained Markov chain model of hierarchic organisations for a given reaction network, which can be used to approximate the behaviour of the original reaction network  ...  chains.  ...  11 (Organisation-oriented interval Markov chain).  ... 
doi:10.1109/tcbb.2018.2804395 pmid:29994367 fatcat:ceomvhxo2bcu5pt4l3km3776lu

Structural features of non-Markovian open quantum systems using quantum chains

András Bodor, Lajos Diósi, Zsófia Kallus, Thomas Konrad
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
Simplest qubit realizations are discussed, and the significance for real system--environment dynamics is also pointed out.  ...  We propose a simple structure for stationary non-Markovian quantum chains in the framework of collisional dynamics of open quantum systems.  ...  FIG. 3 . 3 Selective NM chain: the refinement of the nonselective one in FIG. 4 . 4 Selective one-qubit Markov chain: collisional model.  ... 
doi:10.1103/physreva.87.052113 fatcat:pla2l6ms3rbjfmlzks36p2z45i

Fast Automatic Segmentation of the Esophagus from 3D CT Data Using a Probabilistic Model [chapter]

Johannes Feulner, S. Kevin Zhou, Alexander Cavallaro, Sascha Seifert, Joachim Hornegger, Dorin Comaniciu
2009 Lecture Notes in Computer Science  
Prior shape knowledge of the complete esophagus is modeled using a Markov chain framework, which allows efficient inferrence of the approximate shape from the detected candidate segments.  ...  Automated segmentation of the esophagus in CT images is of high value to radiologists for oncological examinations of the mediastinum.  ...  First, the well known MAP framework for Markov chains is combined with the powerful detector based on the PBT classifier with Haar-like and steerable features [6] .  ... 
doi:10.1007/978-3-642-04268-3_32 fatcat:2h67icrhfvahzeweurxknhfeky

Land Change Modeling Handling with Various Training Dates

Martin Paegelow
2017 Proceedings of the 3rd International Conference on Geographical Information Systems Theory, Applications and Management  
Popular modeling tools for land change simulation, especially those using Markov chains, undertake model training based only on two land use / cover (LUC) maps.  ...  Comparing Markov chain transitions based on two training dates and alternatively performed change rates taking into account all training dates results to important differences.  ...  ACKNOWLEDGEMENTS This work was supported by the BIA2013-43462-P project funded by the Spanish Ministry of Economy and Competitiveness and by the Regional European Fund FED.  ... 
doi:10.5220/0006385003500356 dblp:conf/gistam/Paegelow17 fatcat:nqxikqswavaernxk37tpon5yk4
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