Mathematical Foundations of Computer Science 2004: 29th by Jerzy Tiuryn, Ryszard Rudnicki, Damian Wójtowicz (auth.),

By Jerzy Tiuryn, Ryszard Rudnicki, Damian Wójtowicz (auth.), Jiří Fiala, Václav Koubek, Jan Kratochvíl (eds.)

This quantity comprises the papers awarded on the twenty ninth Symposium on Mat- matical Foundations of desktop technology, MFCS 2004, held in Prague, Czech Republic, August 22–27, 2004. The convention was once geared up through the Institute for Theoretical laptop technology (ITI) and the dept of Theoretical Com- terScienceandMathematicalLogic(KTIML)oftheFacultyofMathematicsand Physics of Charles college in Prague. It used to be supported partially by means of the ecu- pean organization for Theoretical desktop technological know-how (EATCS) and the ecu learn Consortium for Informatics and arithmetic (ERCIM). regularly, the MFCS symposia inspire top of the range study in all branches of theoretical computing device technology. Ranging in scope from automata, f- mal languages, info constructions, algorithms and computational geometry to c- plexitytheory,modelsofcomputation,andapplicationsincludingcomputational biology, cryptography, safety and arti?cial intelligence, the convention o?ers a special chance to researchers from assorted parts to satisfy and current their effects to a common viewers. The scienti?c application of this year’s MFCS happened within the lecture halls of the lately reconstructed construction of the college of arithmetic and P- sics within the ancient middle of Prague, with the well-known Prague citadel and different celebratedhistoricalmonumentsinsight.Theviewfromthewindowswasach- lengingcompetitionforthespeakersinthe?ghtfortheattentionoftheaudience. yet we didn't worry the outcome: end result of the surprisingly difficult pageant for this year’s MFCS, the admitted displays definitely attracted massive in- relaxation. The convention application (and the court cases) consisted of 60 contributed papers chosen via this system Committee from a complete of 167 submissions.

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Extra info for Mathematical Foundations of Computer Science 2004: 29th International Symposium, MFCS 2004, Prague, Czech Republic, August 22-27, 2004. Proceedings

Example text

Without loss of generality we can assume that and for From the asumption it follows immediately that for every and therefore it is sufficient to check (22) for sufficiently small We consider the case (the case is analogous). We have Since we have Therefore we have where Observe that for sufficiently small 20 J. Tiuryn, R. Rudnicki, and D. Wójtowicz and this implies that the series is convergent. Thus the limit exists. It follows that for sufficiently small the limit (22) exists and it is a positive real number.

In order for this to work, we need to ensure that earlier groups do not “delay” the later groups. Basically, if a group starts receiving colors late, it may not matter how efficiently we color it; the resulting coloring will already have become too expensive. [An aside: One may suggest that instead of coloring the groups in sequence – thus effectively delaying all the vertices in a group until all previous groups have been completed – that we try to color the vertices in the group as early as possible, intermixed with the colorings of the earlier groups.

Suppose that and tions from to such that and (i) If (ii) If are arbitrary funcThen is random, is random, A very longstanding question was whether there was a characterization of 1-randomness in terms of plain complexity C. It was known to Martin-Löf that if a real had the property that then was 1-random. 3 We know that Kolmogorov randomness 3 There are some problems with terminology here. Kolmogorov did not actually construct or even name such reals, but he was the first more or less to define randomness for strings via initial segment plain complexity.

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