905,627 research outputs found
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Combinatorics, Probability and Computing
The main theme of this workshop was the use of probabilistic
methods in combinatorics and theoretical computer science. Although
these methods have been around for decades, they are being refined all
the time: they are getting more and more sophisticated and powerful.
Another theme was the study of random combinatorial structures,
either for their own sake, or to tackle extremal questions. The workshop
also emphasized connections between probabilistic combinatorics and
discrete probability
Recommended from our members
Combinatorics, Probability and Computing
One of the exciting phenomena in mathematics in recent years has been the widespread and surprisingly effective use of probabilistic methods in diverse areas. The probabilistic point of view has turned out to b
Quantitative model checking of continuous-time Markov chains against timed automata specifications
We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are\ud
accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations
Alternate Scheme for Optical Cluster-State Generation without Number-Resolving Photon Detectors
We design a controlled-phase gate for linear optical quantum computing by
using photodetectors that cannot resolve photon number. An intrinsic
error-correction circuit corrects errors introduced by the detectors. Our
controlled-phase gate has a 1/4 success probability. Recent development in
cluster-state quantum computing has shown that a two-qubit gate with non-zero
success probability can build an arbitrarily large cluster state with only
polynomial overhead. Hence, it is possible to generate optical cluster states
without number-resolving detectors and with polynomial overhead.Comment: 10 pages, 4 figures, 4 tables; made significant revisions and changed
forma
On the Problem of Computing the Probability of Regular Sets of Trees
We consider the problem of computing the probability of regular languages of
infinite trees with respect to the natural coin-flipping measure. We propose an
algorithm which computes the probability of languages recognizable by
\emph{game automata}. In particular this algorithm is applicable to all
deterministic automata. We then use the algorithm to prove through examples
three properties of measure: (1) there exist regular sets having irrational
probability, (2) there exist comeager regular sets having probability and
(3) the probability of \emph{game languages} , from automata theory,
is if is odd and is otherwise
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