NATO Research Task Group IST-021/RTG-007 interpreted visualisation as a human activity supported by technology. Visualisation is therefore a means by which humans make sense of complex data. The RTG considered visualisation technologies, including display devices and techniques in relation to how they help humans to perform their tasks effectively. The RTG emphasized the human use of the comput...

This is the second paper dedicated to a detailed study of the infinite 3-group ?J= (74 r>, 1’3 = rr;3 = 1, y=(y, CT, 2-l) (a recursive definition to be explained later), which was introduced by the author and Narain Gupta in [2] as a group of automorphisms of an infinite regular tree F. As was shown in [4], Y has the remarkable properties of containing a copy of every finite 3-group, and having...

FTAG, the extension of TAG with feature structures, lags behind other featurebased grammar formalisms in the availability of efficient chart parsers. This is in part because of the complex interaction of adjunction and unification, which makes such parsers inconvenient to implement. We present a novel, simple algebra for feature structures and show how FTAG can be encoded as an Interpreted Regu...

We consider a graph G and a covering G̃ of G and we study the relations of their eigenvalues and heat kernels. We evaluate the heat kernel for an infinite k-regular tree and we examine the heat kernels for general k-regular graphs. In particular, we show that a k-regular graph on n vertices has at most (1 + o(1)) 2 log n kn log k ( (k − 1)k−1 (k2 − 2k)k/2−1 )n spanning trees, which is best possi...

In this paper we present Regular XPath (RXPath), which is a natural extension of XPath with regular expressions over paths that has the same computational properties as XPath: linear-time query evaluation and exponential-time reasoning. To establish these results, we devise a unifying automata-theoretic framework based on two-way weak alternating tree automata. Specifically, we consider automat...

E-generalization computes common generalizations of given ground terms w.r.t. a given equational background theory E. In [Bur05], we had presented a computation approach based on standard regular tree grammar algorithms, and a Prolog prototype implementation. In this report, we present algorithmic improvements, prove them correct and complete, and give some details of an efficiency-oriented imp...

A tree-automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. The finite condensation rank (FC-rank) of a linear ordering measures how far it is away from being dense. We prove that the FC-rank of every tree-automatic linear ordering is below ω. This general...

We address the problem of tight XML schemas and propose regular tree automata to model XML data. We show that the tree automata model is more powerful that the XML DTDs and is closed under main algebraic operations. We introduce the XML query algebra based the tree automata model, and discuss the query optimization and query pruning techniques. Finally, we show the conversion of tree automata s...

Multiple (simple) context-free tree grammars are investigated, where “simple” means “linear and nondeleting”. Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterm...