Deciding the First Levels of the Modal mu Alternation Hierarchy by Formula Construction

We construct, for any sentence of the modal mu calculus Psi, derived sentences in the modal fragment and the fragment without least fixpoints of the modal mu calculus such that Psi is equivalent to a formula in these fragments if and only if it is equivalent to these formulas. The formula without greatest fixpoints that Psi is equivalent to if and only if it is equivalent to any formula without greatest fixpoint is obtained by duality. This yields a constructive proof of decidability of the first levels of the modal mu alternation hierarchy. The blow-up incurred by turning Psi into the modal formula is shown to be necessary: there are modal formulas that can be expressed sub-exponentially more efficiently with the use of fixpoints. For the fragments with only greatest or least fixpoints however, as long as formulas are in disjunctive form, the transformation into a formula syntactically in these fragments does not increase the size of the formula

Estimating capacity and resource allocation in healthcare settings using business process modelling and simulation

Healthcare involves complex decision making from planning to resource management. Resources in hospitals are usually allocated by experienced managers,however, due to an inherent process complexity, decisions are surrounded by uncertainties, variabilities, and constraints. Information Systems must be robust enough to provide support to stakeholders, capable of controlling and support work flows. The present work explores the required synergy when combining business processes with discrete event simulation. The objective is to estimate performance indices and address capacity management of a surgical center as a case study.Postprin

Transfinite Extension of the Mu-Calculus

In [1] Bradfield found a link between finite differences formed by Sigma(2)(0) sets and the mu-arithmetic introduced by Lubarski [7]. We extend this approach into the transfinite: in allowing countable disjunctions we show that this kind of extended mu-calculus matches neatly to the transfinite difference hierarchy of E-2(0) sets. The difference hierarchy is intimately related to parity games. When passing to infinitely many priorities, it might not longer be true that there is a positional winning strategy. However, if such games are derived from the difference hierarchy, this property still holds true