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Applications of metric coinduction
 Proc. 2nd Conf. Algebra and Coalgebra in Computer Science (CALCO 2007), volume 4624 of Lecture Notes in Computer Science
, 2007
"... Abstract. Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One proves a coinduction step showing that some property is preserved by one step of the approximation process, then automatically infers by the ..."
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Abstract. Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One proves a coinduction step showing that some property is preserved by one step of the approximation process, then automatically infers by the coinduction principle that the property holds of the limit object. This can often be used to avoid complicated analytic arguments involving limits and convergence, replacing them with simpler algebraic arguments. This paper examines the application of this principle in a variety of areas, including infinite streams, Markov chains, Markov decision processes, and nonwellfounded sets. These results point to the usefulness of coinduction as a general proof technique. 1
Optimal Coin Flipping
, 2009
"... This paper studies the problem of simulating a coin of arbitrary real bias q with a coin of arbitrary real bias p with minimum loss of entropy. We establish a lower bound that is strictly greater than the informationtheoretic bound. We show that as a function of q, it is an everywherediscontinuous ..."
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This paper studies the problem of simulating a coin of arbitrary real bias q with a coin of arbitrary real bias p with minimum loss of entropy. We establish a lower bound that is strictly greater than the informationtheoretic bound. We show that as a function of q, it is an everywherediscontinuous selfsimilar fractal. We provide efficient protocols that achieve the lower bound to within any desired accuracy for (3 − √ 5)/2 < p < 1/2 and achieve it exactly for p = 1/2. 1
On Prediction and Planning in Partially Observable Markov Decision Processes with Large Observation Sets
, 2011
"... Interested in sequential decision making under uncertainty Agent must infer its “state ” based on observations of environment A larger observation space gives more information, but increases complexity of problem Hardware is cheap and small => many sensors/observations! ..."
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Interested in sequential decision making under uncertainty Agent must infer its “state ” based on observations of environment A larger observation space gives more information, but increases complexity of problem Hardware is cheap and small => many sensors/observations!