First this report presents a restricted set of finite transducers used to synthesise structural time-series constraints described by means of a multi-layered function composition scheme. Second it provides the corresponding synthesised catalogue of structural time-series constraints where each constraint is explicitly described in terms of automata with registers.

Constraints over variable sequences are ubiquitous and many of their propagators have been inspired by dynamic programming (DP). We propose a conceptual framework for designing such propagators: pruning rules, in a functional notation, are refined upon the application of transformation operators to a DP-style formulation of a constraint; a representation of the (tuple) variable domains is picked; and a control of the pruning rules is picked.

We explore the idea of using finite automata to implement new constraints for local search (this is already a successful technique in constraint-based global search). We show how it is possible to maintain incrementally the violations of a constraint and its decision variables from an automaton that describes a ground checker for that constraint. We establish the practicality of our approach idea on real-life personnel rostering problems, and show that it is competitive with the approach of [Pralong, 2007].

Using constraint-based local search, we effectively model and efficiently solve the problem of balancing the traffic demands on portions of the European airspace while ensuring that their capacity constraints are satisfied. The traffic demand of a portion of airspace is the hourly number of flights planned to enter it, and its capacity is the upper bound on this number under which air-traffic controllers can work. Currently, the only form of demand-capacity balancing we allow is ground holding, that is the changing of the take-off times of not yet airborne flights. Experiments with projected European flight plans of the year 2030 show that already this first form of demand-capacity balancing is feasible without incurring too much total delay and that it can lead to a significantly better demand-capacity balance.