Michal Koucký

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We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the <i>cover time</i> - the expected time required to visit every node in a graph at least once - and we show that for a large(More)
Motivated by real world networks and use of algorithms based on random walks on these networks we study the simple random walks on dynamic undirected graphs with fixed underlying vertex set, i.e., graphs which are modified by inserting or deleting edges at every step of the walk. We are interested in the expected time needed to visit all the vertices of(More)
In this paper we introduce a new notion of traversal sequences that we call exploration sequences. Exploration sequences share many properties with the traversal sequences defined in [AKL+], but they also exhibit some new properties. In particular, they have an ability to backtrack, and their random properties are robust under choice of the probability(More)
We show that sets consisting of strings of high Kolmogorov complexity provide examples of sets that are complete for several complexity classes under probabilistic and non-uniform reductions. These sets are provably not complete under the usual many-one reductions. Let RC, RKt, RKS, RKT be the sets of strings x having complexity at least |x|/2, according to(More)
We investigate the question of whether one can characterize complexity classes (such as PSPACE or NEXP) in terms of efficient reducibility to the set of Kolmogorovrandom strings RC. We show that this question cannot be posed without explicitly dealing with issues raised by the choice of universal machine in the definition of Kolmogorov complexity. Among(More)
The effect of dietary supplementation of selenium in an organic form on performance, carcass traits and selenium content in tissues of broiler cockerels Ross 308 was studied. The soya-wheat-maize diet contained 50 mg vitamin E/kg. The experiment was conducted on 810 straight-run broiler cockerels randomly divided into 3 groups: group I – control, without(More)
Abstract. Motivated by real world networks and use of algorithms based on random walks on these networks we study the simple random walks on dynamic undirected graphs, i.e., graphs which are modified by inserting or deleting edges at every step of the walk. We are interested in the expected time needed to visit all the vertices of such a dynamic graph, the(More)
In this paper we show that BPP is truth-table reducible to the set of Kolmogorov random strings R_K. It was previously known that PSPACE, and hence BPP is Turing-reducible to R_K. The earlier proof relied on the adaptivity of the Turing-reduction to find a Kolmogorov-random string of polynomial length using the set R_K as oracle. Our new non-adaptive result(More)
The Hamming and the edit metrics are two common notions of measuring distances between pairs of strings <i>x</i>,<i>y</i> lying in the Boolean hypercube. The edit distance between <i>x</i> and <i>y</i> is defined as the minimum number of character insertion, deletion, and bit flips needed for converting <i>x</i> into <i>y</i>. Whereas, the Hamming distance(More)
The review of intrahepatic cholestasis of pregnancy attempts to summarize the current knowledge of this disease by analysing available literary sources. Intrahepatic cholestasis of pregnancy is a disease that typically appears in the third trimester of pregnancy, sometimes already at the end of the second trimester of pregnancy. The main symptom of the(More)