Weak MSO+U with Path Quantifiers over Infinite Trees

This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.Comment: version of an ICALP 2014 paper with appendice

An edge-weighted hook formula for labelled trees

A number of hook formulas and hook summation formulas have previously appeared, involving various classes of trees. One of these classes of trees is rooted trees with labelled vertices, in which the labels increase along every chain from the root vertex to a leaf. In this paper we give a new hook summation formula for these (unordered increasing) trees, by introducing a new set of indeterminates indexed by pairs of vertices, that we call edge weights. This new result generalizes a previous result by F\'eray and Goulden, that arose in the context of representations of the symmetric group via the study of Kerov's character polynomials. Our proof is by means of a combinatorial bijection that is a generalization of the Pr\"ufer code for labelled trees.Comment: 25 pages, 9 figures. Author-produced copy of the article to appear in Journal of Combinatorics, including referee's suggestion

Quantifying Timing Leaks and Cost Optimisation

We develop a new notion of security against timing attacks where the attacker is able to simultaneously observe the execution time of a program and the probability of the values of low variables. We then show how to measure the security of a program with respect to this notion via a computable estimate of the timing leakage and use this estimate for cost optimisation.Comment: 16 pages, 2 figures, 4 tables. A shorter version is included in the proceedings of ICICS'08 - 10th International Conference on Information and Communications Security, 20-22 October, 2008 Birmingham, U

Cyclic schedules for r irregularly occurring event

Consider r irregular polygons with vertices on some circle. Authors explains how the polygons should be arranged to minimize some criterion function depending on the distances between adjacent vertices. A solution of this problem is given. It is based on a decomposition of the set of all schedules into local regions in which the optimization problem is convex. For the criterion functions minimize the maximum distance and maximize the minimum distance the local optimization problems are related to network flow problems which can be solved efficiently. If the sum of squared distances is to be minimized a locally optimal solution can be found by solving a system of linear equations. For fixed r the global problem is polynomially solvable for all the above-mentioned objective functions. In the general case, however, the global problem is NP-hard