Deformation spaces of trees

Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the other). Examples include Culler-Vogtmann's outer space, and spaces of JSJ decompositions. We discuss what features are common to trees in a given deformation space, how to pass from one tree to all other trees in its deformation space, and the topology of deformation spaces. In particular, we prove that all deformation spaces are contractible complexes.Comment: Update to published version. 43 page

Data-oriented parsing and the Penn Chinese treebank

We present an investigation into parsing the Penn Chinese Treebank using a Data-Oriented Parsing (DOP) approach. DOP comprises an experience-based approach to natural language parsing. Most published research in the DOP framework uses PStrees as its representation schema. Drawbacks of the DOP approach centre around issues of efficiency. We incorporate recent advances in DOP parsing techniques into a novel DOP parser which generates a compact representation of all subtrees which can be derived from any full parse tree. We compare our work to previous work on parsing the Penn Chinese Treebank, and provide both a quantitative and qualitative evaluation. While our results in terms of Precision and Recall are slightly below those published in related research, our approach requires no manual encoding of head rules, nor is a development phase per se necessary. We also note that certain constructions which were problematic in this previous work can be handled correctly by our DOP parser. Finally, we observe that the ‘DOP Hypothesis’ is confirmed for parsing the Penn Chinese Treebank

Proving Continuity of Coinductive Global Bisimulation Distances: A Never Ending Story

We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the cost of transformations: how much we need to modify one of the compared processes to obtain the other. Our original definition only covered finite processes, but a coinductive approach allows us to extend it to cover infinite but finitary trees. After having shown many interesting properties of our distance, it was our intention to prove continuity with respect to projections, but unfortunately the issue remains open. Nonetheless, we have obtained several partial results that are presented in this paper.Comment: In Proceedings PROLE 2015, arXiv:1512.0617

The outer space of a free product

We associate a contractible ``outer space'' to any free product of groups G=G_1*...*G_q. It equals Culler-Vogtmann space when G is free, McCullough-Miller space when no G_i is Z. Our proof of contractibility (given when G is not free) is based on Skora's idea of deforming morphisms between trees. Using the action of Out(G) on this space, we show that Out(G) has finite virtual cohomological dimension, or is VFL (it has a finite index subgroup with a finite classifying space), if the groups G_i and Out(G_i) have similar properties. We deduce that Out(G) is VFL if G is a torsion-free hyperbolic group, or a limit group (finitely generated fully residually free group).Comment: Updated reference. To appear in Proc. L.M.

Whitehead moves for G-trees

We generalize the familiar notion of a Whitehead move from Culler and Vogtmann's Outer space to the setting of deformation spaces of G-trees. Specifically, we show that there are two moves, each of which transforms a reduced G-tree into another reduced G-tree, that suffice to relate any two reduced trees in the same deformation space. These two moves further factor into three moves between reduced trees that have simple descriptions in terms of graphs of groups. This result has several applications.Comment: v1: 9 pages; v2: 10 pages, minor revisions and one added referenc