Shuffling and Unshuffling

We consider various shuffling and unshuffling operations on languages and words, and examine their closure properties. Although the main goal is to provide some good and novel exercises and examples for undergraduate formal language theory classes, we also provide some new results and some open problems

Proof Nets and the Complexity of Processing Center-Embedded Constructions

This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can usually be restated in terms of geometrical constraints on proof nets. The paper ends with a discussion of the relationship between these constraints and incremental semantic interpretation.Comment: To appear in Proceedings of LACL 95; uses epic.sty, eepic.sty, rotate.st

Groups, Graphs, Languages, Automata, Games and Second-order Monadic Logic

In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic

Two characterisation results of multiple context-free grammars and their application to parsing

In the first part of this thesis, a Chomsky-Schützenberger characterisation and an automaton characterisation of multiple context-free grammars are proved. Furthermore, a framework for approximation of automata with storage is described. The second part develops each of the three theoretical results into a parsing algorithm

Rational cross-sections, bounded generation and orders on groups

We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Specifically, our examples are extensions of infinite torsion groups, groups of Grigorchuk type, wreath products similar to $C_2\wr(C_2\wr \mathbb Z)$ and $\mathbb Z\wr F_2$, a group of permutations of $\mathbb Z$, and a finitely presented HNN extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word problem and without rational cross-sections. It is also not autostackable, and has no left-regular complete rewriting system.Comment: Comments are welcome! 38 pages, 23 figure

Cosets in inverse semigroups and inverse subsemigroups of finite index

The index of a subgroup of a group counts the number of cosets of that subgroup. A subgroup of finite index often shares structural properties with the group, and the existence of a subgroup of finite index with some particular property can therefore imply useful structural information for the overgroup. Although a developed theory of cosets in inverse semigroups exists, it is defined only for closed inverse subsemigroups, and the structural correspondences between an inverse semigroup and a closed inverse subsemigroup of finte index are much weaker than in the group case. Nevertheless, many aspects of this theory remain of interest, and some of them are addressed in this thesis. We study the basic theory of cosets in inverse semigroups, including an index formula for chains of subgroups and an analogue of M. Hall’s Theorem on counting subgroups of finite index in finitely generated groups. We then look at specific examples, classifying the finite index inverse subsemigroups in polycyclic monoids and in graph inverse semigroups. Finally, we look at the connection between the properties of finite generation and having finte index: these were shown to be equivalent for free inverse monoids by Margolis and Meakin