By Solomon Marcus (auth.), Michael J. Dinneen, Bakhadyr Khoussainov, André Nies (eds.)
This Festschrift quantity has been released in honor of Cristian Calude at the party of his sixtieth birthday and includes contributions from invited audio system and usual papers provided on the foreign Workshop on Theoretical laptop technological know-how, WTCS 2012, held in Auckland, New Zealand, in February 2012.
Cristian Calude has made an important contribution to analyze in desktop technological know-how idea. besides early paintings via Chaitin, Kučera, Kurtz, Solovay, and Terwijn his papers released within the mid-1990s together with Khoussainov, Hertling, and Wang laid the basis for the advance of contemporary concept of algorithmic randomness. His paintings used to be crucial for developing the prime position of recent Zealand during this quarter.
The learn pursuits of Cristian Calude are mirrored within the themes coated via the 32 papers incorporated during this ebook, particularly: algorithmic info conception, algorithms, automata and formal languages, computing and traditional sciences, computability and purposes, common sense and purposes, philosophy of computation, physics and computation, and unconventional versions of computation. they've been geared up into 4 elements. the 1st half contains papers discussing his existence achievements. this can be via papers within the 3 basic parts of complexity, computability, and randomness; physics, philosophy (and logic), and computation; and algorithms, automata, and formal versions (including unconventional computing).
Read or Download Computation, Physics and Beyond: International Workshop on Theoretical Computer Science, WTCS 2012, Dedicated to Cristian S. Calude on the Occasion of His 60th Birthday, Auckland, New Zealand, February 21-24, 2012, Revised Selected and Invited Papers PDF
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Extra resources for Computation, Physics and Beyond: International Workshop on Theoretical Computer Science, WTCS 2012, Dedicated to Cristian S. Calude on the Occasion of His 60th Birthday, Auckland, New Zealand, February 21-24, 2012, Revised Selected and Invited Papers
He has joint papers with each of them, and also with two others who were not his direct professors, Virgil C˘az˘anescu and Monica Dumitrescu. In Auckland he continued to cooperate with his department colleagues, in both theory and applied computer science and mathematics; it seems that he has the highest number of joint papers with colleagues in his department. He had, and continue to have, a strong interaction with colleagues from his generation, particularly, G. P˘ aun and S. Istrail. 10 The mother of his life-long friend Dan Botezatu, a distinguished medical doctor.
So randomness is upward-closed and therefore complete lower semicomputable reals are random. Remark. The second part can be reformulated: if α and β are lower semicomputable reals and at least one of them is random, then the sum α + β is random, too. The reverse is also true: if both α and β are non-random, then α + β is not random. ) 4 Randomness and Prediction Game Before proving the reverse implication, let us make a digression and look more closely at the last argument. Consider the following game: an observer watches an increasing sequence of rationals (given one by one) and from time to time makes predictions of the following type: “the sequence will never increase by more than δ ” (compared to its current value).
The definition of Martin-L¨of randomness guarantees that for every ε > 0 one can find an effectively open set that has measure less than ε and covers all non-random reals. ) Then take the minimal element α in a closed set [0, 1] \ U. This number is random (by definition) and lower semicomputable: compactness implies that any segment [0, r] with rational r < α is covered by finitely many intervals of U and thus all such r’s can be enumerated. Second, we prove that randomness is upward-closed: if α β and α is random, then β is random.