A Guide To Entropy And The Second Law Of Thermodynamics by Jakob Yngvason, Elliott H.Lieb

By Jakob Yngvason, Elliott H.Lieb

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Paul can win n≥1 (p + 1) the unbounded searching problem with p-parallel comparison questions with f (x) rounds of p questions. Spencer and Winkler [77] considered linearly bounded errors, the result can be found in section 12. 15. Optimal strategies with minimum adaptiveness In many practical situations the goal is to find searching strategies with minimum adaptiveness. That means that many questions can be asked without feedback. Unfortunately, in general totally non-adaptive strategies are much worse (see for example [56]).

V is called a k-state if k questions are left. 2. Let v = |Sl |, . . , |S0 | be an arbitrary state and let M0 , . . , Mq−1 be the next partition used by Paul. ” by [x] = ⎤ ⎡ xl0 . . xl(q−1) ⎢ .. ⎥, where x = ⎣ ... . |Xji |. 0 i,j . (q−1) x00 . . x0(q−1) question-matrix. 3. The state s can be reduced to the states a1 , a2 , . . , aq if there exists a question [x] such that a1 , a2 , . . , aq are possible states after this question. 4. 1. A 0-state x is called winning if losing. l i=0 xi ≤ 1.

Paul regards each answer as a vote against a certain subset of words. Paul asks n questions and Carole is allowed to lie at most l times. 1. If Paul has q questions left, in the situation described above for all j ∈ {1, . . 2. We call the vector v = µ(Xlq ), . . , µ(X0q ) = (vl , vl−1 , . . , v0 ) a q-state (of the game), where µ is the measure of Xiq . 3. We say the state x can be reduced to the states y and z, if ∃u, v ≥ 0 : 50 C. Deppe 1. x = u + v 2. yi = ui + vi+1 3. 4. 1. We call e = (e0 , .

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