We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow ε-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain tree-automatic whence their first-order logic theories are decidable. As a corollary we obtain the tree-automaticity of the second level of the Caucal-hierarchy.

We prove that it is NP-complete to decide whether a given (3-dimensional) simplicial complex is collapsible. This work extends a result of Malgouyres and Francés showing that it is NP-complete to decide whether a given simplicial complex collapses to a 1-complex.

We present a pinned insect manipulator (IMp) constructed of LEGO® building bricks with two axes of movement and two axes of rotation. In addition we present three variants of the IMp to emphasise the modular design, which facilitates resizing to meet the full range of pinned insect specimens, is fully customizable, collapsible, affordable and does not require specialist tools or knowledge to as...

We show that collapsible deterministic second level pushdown automata can recognize more languages than deterministic second level pushdown automata (without collapse). This implies that there exists a tree generated by a second level recursion scheme which is not generated by any second level safe recursion scheme. 1998 ACM Subject Classification F.4.3 Formal Languages Digital Object Identifie...