330 research outputs found
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
and , a group of permutations of
, 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
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