Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

Geodesic planes in a geometrically finite end and the halo of a measured lamination

Recent works [MMO1, arXiv:1802.03853, arXiv:1802.04423, arXiv:2101.08956] have shed light on the topological behavior of geodesic planes in the convex core of a geometrically finite hyperbolic 3-manifolds $M$ of infinite volume. In this paper, we focus on the remaining case of geodesic planes outside the convex core of $M$, giving a complete classification of their closures in $M$. In particular, we show that the behavior is different depending on whether exotic roofs exist or not. Here an exotic roof is a geodesic plane contained in an end $E$ of $M$, which limits on the convex core boundary $\partial E$, but cannot be separated from the core by a support plane of $\partial E$. A necessary condition for the existence of exotic roofs is the existence of exotic rays for the bending lamination. Here an exotic ray is a geodesic ray that has finite intersection number with a measured lamination $\mathcal{L}$ but is not asymptotic to any leaf nor eventually disjoint from $\mathcal{L}$. We establish that exotic rays exist if and only if $\mathcal{L}$ is not a multicurve. The proof is constructive, and the ideas involved are important in the construction of exotic roofs. We also show that the existence of geodesic rays satisfying a stronger condition than being exotic, phrased in terms of only the hyperbolic surface $\partial E$ and the bending lamination, is sufficient for the existence of exotic roofs. As a result, we show that geometrically finite ends with exotic roofs exist in every genus. Moreover, in genus $1$, when the end is homotopic to a punctured torus, a generic one (in the sense of Baire category) contains uncountably many exotic roofs.Comment: 42 pages, 14 figures, 39 pages without appendix and references. Supersedes arXiv:2105.0037

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first