@string{brics =	"{BRICS}"}
@string{daimi =	"Department of Computer Science, University of Aarhus"}
@string{iesd  =	"Department of Mathematics and Computer Science, Aalborg University"}
@string{rs    =	"Research Series"}
@string{ns    =	"Notes Series"}
@string{ls    =	"Lecture Series"}
@string{ds    =	"Dissertation Series"}

@TechReport{BRICS-DS-96-4,
author = 	 "Torben Bra{\"u}ner",
title = 	 "An Axiomatic Approach to Adequacy",
institution =  brics,
year = 	 1996,
type = 	 ds,
number = 	 "DS-96-4",
month = 	 nov,
note =	 "Ph.D. thesis. 168~pp",
abstract =	 "This thesis studies adequacy for PCF-like languages in a
general categorical framework. An adequacy result relates
the denotational semantics of a program to its
operational semantics; it typically states that a program
terminates whenever the interpretation is non-bottom. The
main concern is to generalise to a linear version of PCF
the adequacy results known for standard PCF, keeping in
mind that there exists a Girard translation from PCF to
linear PCF with respect to which the new constructs
should be sound. General adequacy results have usually
been obtained in order-enriched categories, that is,
categories where all hom-sets are typically cpos, maps
are assumed to be continuous and fixpoints are
interpreted using least upper bounds. One of the main
contributions of the thesis is to propose a completely
different approach to the problem of axiomatising those
categories which yield adequate semantics for PCF and
linear PCF. The starting point is that the only
unavoidable assumption for dealing with adequacy is the
existence, in any object, of a particular undefined''
point denoting the non-terminating computation of the
corresponding type; hom-sets are pointed sets, and this
is the only required structure. In such a category of
pointed objects, there is a way of axiomatising fixpoint
operators: They are maps satisfying certain equational
axioms, and furthermore, satisfying a very natural
non-equational axiom called rational openness. It is
shown that this axiom is sufficient, and in a precise
sense necessary, for adequacy. The idea is developed in
the intuitionistic case (standard PCF) as well as in the
linear case (linear PCF), which is obtained by augmenting
a Curry-Howard interpretation of Intuitionistic Linear
Logic with numerals and fixpoint constants, appropriate
for the linear context. Using instantiations to concrete
models of the general adequacy results, various purely
syntactic properties of linear PCF are proved to hold",
}

@TechReport{BRICS-DS-96-3,
author = 	 "Lars Arge",
title = 	 "Efficient External-Memory Data Structures and Applications",
institution =  brics,
year = 	 1996,
type = 	 ds,
number = 	 "DS-96-3",
month = 	 aug,
note =	 "Ph.D. thesis. xii+169~pp",
abstract =	 "\bgroup\def\a{algorithms}
In this thesis we study the Input/Output (I/O) complexity
of large-scale problems arising e.g. in the areas of
database systems, geographic information systems, VLSI
design systems and computer graphics, and design
I/O-efficient \a{} for them.\bibpar
A general theme in our work is to design I/O-efficient
\a{} through the design of I/O-efficient data
structures. One of our philosophies is to try to design
I/O \a{} from internal memory \a{} by
exchanging the data structures used in internal memory
with their external memory counterparts. The results in
the thesis include a technique for transforming an
internal memory tree data structure into an external data
structure which can be used in a {\em batched\/} dynamic
setting, that is, a setting where we for example do not
require that the result of a search operation is returned
immediately. Using this technique we develop batched
dynamic external versions of the (one-dimensional)
range-tree and the segment-tree and we develop an
external priority queue. These structures can be used in
standard internal memory sorting \a{} and
\a{} for problems involving geometric objects. The
latter has applications to VLSI design. Using the
priority queue we improve upon known I/O \a{} for
fundamental graph problems, and develop new efficient
\a{} for the graph-related problem of ordered
binary-decision diagram manipulation. Ordered
binary-decision diagrams are the state-of-the-art data
structure for boolean function manipulation and they are
extensively used in large-scale applications like logic
circuit verification.\bibpar
Combining our batched dynamic segment tree with the novel
technique of external-memory fractional cascading we
develop I/O-efficient \a{} for a large number of
geometric problems involving line segments in the plane,
with applications to geographic informations
systems. Such systems frequently handle huge amounts of
spatial data and thus they require good use of
external-memory techniques.\bibpar
We also manage to use the ideas in the batched dynamic
segment tree to develop on-line'' external data
structures for a special case of two-dimensional range
searching with applications to databases and constraint
logic programming. We develop an on-line external version
of the segment tree, which improves upon the previously
best known such structure, and an optimal on-line
external version of the interval tree. The last result
settles an important open problem in databases and I/O
\a. In order to develop these structure we use a
novel balancing technique for search trees which can be
regarded as weight-balancing of B-trees.\bibpar
Finally, we develop a technique for transforming internal
memory lower bounds to lower bounds in the I/O model, and
we prove that our new ordered binary-decision diagram
manipulation \a{} are asymptotically optimal among
a class of \a{} that include all know manipulation
\a\egroup.",
}

@TechReport{BRICS-DS-96-2,
author = 	 "Allan Cheng",
title = 	 "Reasoning About Concurrent Computational Systems",
institution =  brics,
year = 	 1996,
type = 	 ds,
number = 	 "DS-96-2",
month = 	 aug,
note =	 "Ph.D. thesis. xiv+229~pp",
abstract =	 "This thesis consists of three parts. The first presents
contributions in the field of verification of finite
state concurrent systems, the second presents
contributions in the field of behavioural reasoning about
concurrent systems based on the notions of behavioural
preorders and behavioural equivalences, and, finally, the
third presents contributions in the field of set
constraints.\bibpar
In the first part, we study the computational complexity
of several standard verification problems for 1-safe
Petri nets and some of its subclasses. Our results
provide the first systematic study of the computational
complexity of these problems.\bibpar
We then investigate the computational complexity of a
more general verification problem, model-checking, when
an instance of the problem consists of a formula and a
description of a system whose state space is at most
exponentially larger than the description.\bibpar
We continue by considering the problem of performing
model-checking relative to a partial order semantics of
concurrent systems, in which not all possible sequences
of actions are considered relevant. We provide the first,
to the best of our knowledge, set of sound and complete
tableau rules for a CTL-like logic interpreted under
progress fairness assumptions. \bibpar
In the second part, we investigate Joyal, Nielsen, and
Winskel's proposal of spans of open maps as an abstract
category-theoretic way of adjoining a bisimulation
equivalence, ${\cal P}$-bisimilarity, to a category of
models of computation ${\cal M}$. We show that a
representative selection of well-known bisimulations and
behavioural equivalences can be captured in the setting
of spans of open maps.\bibpar
We then define the notion of functors being ${\cal P}$-factorisable and show how this ensures that ${\cal P}$-bisimilarity is a congruence with respect to such
functors. \bibpar
In the last part we investigate set constraints. Set
constraints are inclusion relations between expressions
denoting sets of ground terms over a ranked
alphabet. They are typically derived from the syntax of a
program and solutions to them can yield useful
information for, e.g., type inference, implementations,
and optimisations.\bibpar
We provide a complete Gentzen-style axiomatisation for
sequents $\Phi\vdash\Psi$, where $\Phi$ and $\Psi$ are
finite sets of set constraints, based on the axioms of
termset algebra. We show that the deductive system is
complete for the restricted sequents $\Phi\vdash\bot$
over standard models, incomplete for general sequents
$\Phi\vdash\Psi$ over standard models, but complete for
general sequents over set-theoretic termset
algebras.\bibpar
We then continue by investigating Kozen's rational
spaces.  We give several interesting results, among
others a Myhill-Nerode like characterisation of rational
points.",
}

@TechReport{BRICS-DS-96-1,
author = 	 "Urban Engberg",
title = 	 "Reasoning in the Temporal Logic of Actions --- The design
and implementation of an interactive computer system",
institution =  brics,
year = 	 1996,
type = 	 ds,
number = 	 "DS-96-1",
month = 	 aug,
note =	 "Ph.D. thesis. xvi+222~pp",
abstract =	 "Reasoning about algorithms stands out as an essential
challenge of computer science.  Much work has been put
into the development of formal methods, within recent
years focusing especially on concurrent algorithms.  The
Temporal Logic of Actions (TLA) is one of the formal
frameworks that has been the result of such research.  In
TLA a system and its properties may be specified as
logical formulas, allowing the application of reasoning
without any intermediate translation.  Being a
linear-time temporal logic, it easily expresses liveness
as well as safety properties.\bibpar
TLP, the TLA Prover, is a system developed by the author
for doing mechanical reasoning in TLA.  TLP is a complex
system that combines different reasoning techniques to be
able to handle verification of real systems.  It uses the
Larch Prover as its main verification back-end, but as
well makes it possible to utilize results provided by
other back-ends, such as an automatic linear-time
temporal logic checker for finite-state systems.
Specifications to be verified within the TLP system are
written in a dedicated language, an extension of pure
TLA.  The language as well contains syntactical
constructs for representing natural deduction proofs, and
a separate language for defining methods to be applied
during verification.  With the TLP translators and
interactive front-end, it is possible to write
specifications and incrementally develop mechanically
verifiable proofs in a fashion that has not been seen
before.",