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1

Maximizing T-complexity

Clark G., Teutsch J.

Fundamenta Informaticae

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2015

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Vol. 139, nr 1

1--19

EN

We investigate Mark Titchener’s T-complexity, an algorithm which measures the information content of finite strings. After introducing the T-complexity algorithm, we turn our attention to a particular class of “simple” finite strings. By exploiting special properties of simple strings, we obtain a fast algorithm to compute the maximum T-complexity among strings of a given length, and our estimates of these maxima show that T-complexity differs asymptotically from Kolmogorov complexity. Finally, we examine how closely de Bruijn sequences resemble strings with high Tcomplexity.

2

Deterministic One-Way Turing Machines with Sublinear Space

Kutrib M., Provillard J., Vaszil G., Wendlandt M.

Fundamenta Informaticae

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2015

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Vol. 136, nr 1/2

139--155

EN

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The class of functions space constructible by such machines is investigated, and it is shown that every function f that is space constructible by a deterministic two-way Turing machine, is space constructible by a strongly f space-bounded deterministic one-way Turing machine as well. We prove that the restricted mode coincides with the strong mode for space constructible functions. The known infinite, dense, and strict hierarchy of strong space complexity classes is derived also for the weak mode by Kolmogorov complexity arguments. Finally, closure properties under AFL operations, Boolean operations and reversal are shown.

3

Text comparison using data compression

Platos J., Prilepok M., Snasel V.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 11

59-61

EN

Similarity detection is very important in the field of spam detection, plagiarism detection or topic detection. The main algorithm for comparison of text document is based on the Kolmogorov Complexity, which is one of the perfect measures for computation of the similarity of two strings in defined alphabet. Unfortunately, this measure is incomputable and we must define several approximations which are not metric at all, but in some circumstances are close to this behaviour and may be used in practice.

PL

W artykule omówiono metody rozpoznawania podobieństwa tekstu. Głównie używanym algorytmem jest Kolmogotov Complexity. Głównym ograniczeniem jest brak możliwości dane algorytmu są trudne do dalszego przetwarzania numerycznego – zaproponowano szereg aproksymacji.

4

A Simple Proof of Miller-Yu Theorem

Bienvenu L., Merkle W., Shen A.

Fundamenta Informaticae

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2008

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Vol. 83, nr 1-2

21-24

EN

A few years ago a nice criterion of Martin-Löf randomness in terms of plain (neither prefix nor monotone) Kolmogorov complexity was found (among many other results, it is published in [5]). In fact Martin-Löf came rather close to the formulation of this criterion around 1970 (see [4] and [7], p. 98); a version of it that involves both plain and prefix complexity was proven by Gacs in 1980 ([2], remark after corollary 5.4 on p. 391). We provide a simple proof of this criterion that uses only elementary arguments very close to the original proof of Levin-Schnorr criterion of randomness (1973) in terms of monotone complexity ([3, 6]).