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

  author = 	 "Sobocinski, Pawe{\l}",
  title = 	 "Deriving Process Congruences from Reaction
  institution =  brics,
  year = 	 2004,
  type = 	 ds,
  number = 	 "DS-04-6",
  address = 	 daimi,
  month = 	 dec,
  note = 	 "PhD thesis. xii+216~pp",
  comment = 	 "Defence: December~3, 2004",
  abstract = 	 "This thesis is concerned with the development
                  of a theory which, given a formalism with a
                  reduction semantics, allows the derivation of a
                  canonical labelled transition system on which
                  bisimilarity as well as other other
                  equivalences are congruences; provided that the
                  contexts of the formalism form a category which
                  has certain colimits.\bibpar
                  We shall begin by extending Leifer and Milner's
                  theory of reactive systems to a 2-categorical
                  setting. This development is motivated by the
                  common situation in which the contexts of a
                  reactive system contain non-trivial algebraic
                  structure with an associated notion of context
                  isomorphism. Forgetting this structure often
                  leads to problems and we shall show that the
                  theory can be extended smoothly, retaining this
                  useful information as well as the congruence
                  Technically, the generalisation includes
                  defining the central notion of
                  groupoidal-relative-pushout (GRPO)
                  (categorically: a bipushout in a pseudoslice
                  category), which turns out to provide a
                  suitable generalisation of Leifer and Milner's
                  relative pushout (RPO). The congruence theorems
                  are then reproved in this more general setting.
                  We shall also show how previously introduced
                  alternative solutions to the problem of
                  forgetting the two-dimensional structure can be
                  reduced to the 2-categorical approach.\bibpar
                  Secondly, we shall construct GRPOs in settings
                  which are general enough to allow the theory to
                  be applied to useful, previously studied
                  examples. We shall begin by constructing GRPOs
                  in a category whose arrows correspond closely
                  to the contexts a simple process calculus, and
                  extend this construction further to cover the
                  category of bunch contexts, studied previously
                  by Leifer and Milner. The constructions use the
                  structure of extensive categories.\bibpar
                  We shall argue that cospans provide an
                  interesting notion of ``generalised contexts''.
                  In an effort to find a natural class of
                  categories which allows the construction of
                  GRPOs in the corresponding cospan bicategory,
                  we shall introduce the class of adhesive
                  categories. As extensive categories have
                  well-behaved coproducts, so adhesive categories
                  have well-behaved pushouts along monomorphisms.
                  Adhesive categories also turn out to be a
                  useful tool in the study and generalisation of
                  the theory of double-pushout graph
                  transformation systems, indeed, such systems
                  have a rich rewriting theory when defined over
                  adhesive categories.\bibpar
                  Armed with the theory of adhesive categories,
                  we shall present a construction of GRPOs in
                  input-linear cospan bicategories. As an
                  immediate application, we shall shed light on
                  as well as extend the theory of rewriting via
                  borrowed contexts, due to Ehrig and K{\"o}nig.
                  Secondly, we shall examine the implications of
                  the construction for Milner's bigraphs."
  author =	 "Skjernaa, Bjarke",
  title =	 "Exact Algorithms for Variants of Satisfiability and
                  Colouring Problems",
  institution =	 brics,
  year =	 2004,
  type =	 ds,
  number =	 "DS-04-5",
  address =	 daimi,
  month =	 nov,
  note =	 "PhD thesis. x+112~pp",
  comment =	 "Defence: November~11, 2004",
  abstract =	 "This dissertation studies exact algorithms for
                  various hard problems and give an overview of not
                  only results but also the techniques used.\bibpar In
                  the first part we focus on Satisfiability and
                  several variants of Satisfiability. We present some
                  historical techniques and results. Our main focus in
                  the first part is on a particular variant of
                  Satisfiability, Exact Satisfiability. Exact
                  Satisfiability is the variant of Satisfiability
                  where a clause is satisfied if it contains exactly
                  one \textit{true} literal. We present an algorithm solving
                  Exact Satisfiability in time $O(2^{0.2325n})$, and
                  an algorithm solving Exact 3-Satisfiability, the
                  variant of Exact Satisfiability where each clause
                  contains at most three literals, in time
                  $O(2^{0.1379n})$. In these algorithms we use a new
                  concept of \emph{$k$-sparse} formulas, and we
                  present a new technique called \emph{splitting
                  loosely connected formulas}, although we do not use
                  the technique in the algorithms. \bibpar We present
                  a new program which generates algorithms and
                  corresponding upper bound proofs for variants of
                  Satisfiability, and in particular Exact
                  Satisfiability. The program uses several new
                  techniques which we describe and compare to the
                  techniques used in three other programs generating
                  algorithms and upper bound proofs.\bibpar In the
                  second part we focus on another class of NP-complete
                  problems, colouring problems. We present several
                  algorithms for 3-Colouring, and discuss
                  $k$-Colouring in general. We also look at the
                  problem of determining the chromatic number of a
                  graph, which is the minimum number, $k$, such that
                  the graph is $k$-colourable. We present a technique
                  using maximal bipartite subgraphs to solve
                  $k$-Colouring, and prove two bounds on the maximum
                  possible number of maximal bipartite subgraphs of a
                  graph with $n$ vertices: a lower bound of
                  $\Omega(1.5926^n)$ and an upper bound of
                  $O(1.8612^n)$. We also present a recent improvement
                  of the upper bound by Byskov and Eppstein, and show
                  a number of applications of this in colouring
                  problems.\bibpar In the last part of this
                  dissertation we look at a class of problems
                  unrelated to the above, Graph Distinguishability
                  problems. DIST$_k$ is the problem of determining if
                  a graph can be coloured with $k$ colours, such that
                  no non-trivial automorphism of the graph preserves
                  the colouring. We present some results on
                  determining the distinguishing number of a graph,
                  which is the minimum $k$, such that the graph is in
                  DIST$_k$. We finish by proving a new result which
                  shows that DIST$_k$ can be reduced to DIST$_l$ for
                  various values of $k$ and $l$",
  linkhtmlabs =  "",
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  author = 	 "Byskov, Jesper Makholm",
  title = 	 "Exact Algorithms for Graph Colouring and Exact
  institution =  brics,
  year = 	 2004,
  type = 	 ds,
  number = 	 "DS-04-4",
  address = 	 daimi,
  month = 	 nov,
  note = 	 "PhD thesis",
  comment = 	 "Defence: November~11, 2004",
  abstract = 	 "This dissertation contains results within the field of exact
algorithms for NP-hard problems. We give an overview of the major
results within the field as well as the main techniques used. Then we
present new exact algorithms for various graph colouring problems and
for two variants of \textsc{Exact Satisfiability} (\textsc{XSAT}).\bibpar

In graph colouring, we first look at the problem of enumerating all
maximal independent sets of a graph. This is not an NP-hard problem,
but algorithms for this problem are useful for solving other graph
colouring problems. Moon and Moser (1965) have given tight upper
bounds on the number of maximal independent sets in a graph, and there
exists a number of algorithms for enumerating them all. We look at the
extended problems of enumerating all maximal independent sets of size
equal to $k$, of size at most~$k$ and of size at least $k$ for $1\leq
k\leq n$. We give tight upper bounds on the number of such sets and
give algorithms for enumerating them all in time within a polynomial
factor of these upper bounds, thereby extending earlier work of
Eppstein (2003a). Then we look at algorithms for enumerating all
maximal bipartite subgraphs of a graph. We give upper and lower bounds
on the number of maximal bipartite subgraphs and an algorithm for
enumerating all such subgraphs, but the bounds are not tight. The work
on maximal bipartite subgraphs is from two different papers, one with
B.~A.~Madsen and B.~Skjernaa and the other with D.~Eppstein. Finally,
we give algorithms for enumerating all maximal $k$-colourable
subgraphs of a graph for $k\geq 3$. These algorithms all run in time
$\omega(2^n)$ and we have no $o(2^n)$ upper bound on the number of
maximal $k$-colourable subgraphs for $k\geq 3$. The algorithm for
$k=3$ is from joint work with D.~Eppstein. We use all the
above-mentioned algorithms in new algorithms for \textsc{4-Colouring},
\textsc{5-Colouring} and \textsc{6-Colouring} using ideas of Lawler
(1976). Some of these algorithms are also joint work with D.~Eppstein.
We also improve an algorithm of Eppstein (2003a) for the
\textsc{Chromatic Number} problem.\bibpar

We also give new, improved algorithms for \textsc{XSAT} as well as
\textsc{X3SAT}, the variant where each clause contains at most three
literals. Our improvements come from three sources. First, we discover
new reduction rules which allow us to get rid of more formulas by
replacing them by simpler formulas. Next, we extend the case analyses
of previous algorithms to distinguish between more cases. Finally, we
introduce a new concept called sparse formulas. \textsc{XSAT} can be
solved in polynomial time if no variable occurs more than twice in the
formula. We call a formula sparse, if the number of variables
occurring more than twice is small. Such formulas we solve by trying
all possible truth assignments to the variables occurring more than
twice. Then the remaining parts of the formulas contain only variables
occurring at most twice, so they can be solved in polynomial time.
Both algorithms are joint work with B.~A.~Madsen and B.~Skjernaa"
  author =	 "Groth, Jens",
  title =	 "Honest Verifier Zero-knowledge Arguments Applied",
  institution =	 brics,
  year =	 2004,
  type =	 ds,
  number =	 "DS-04-3",
  address =	 daimi,
  month =	 oct,
  note =	 "PhD thesis. xii+119~pp",
  comment =	 "Defence: October~15, 2004",
  abstract =	 "We apply honest verifier zero-knowledge arguments to
                  cryptographic protocols for non-malleable
                  commitment, voting, anonymization and group
                  signatures. For the latter three the random oracle
                  model can be used to make them
                  non-interactive. Unfortunately, the random oracle
                  model is in some ways unreasonable, we present
                  techniques to reduce the dependence on it.\bibpar
                  Several voting schemes have been suggested in the
                  literature, among them a class of efficient
                  protocols based on homomorphic threshold
                  encryption. Voters encrypt their votes, and using
                  the homomorphic property of the cryptosystem we can
                  get an encryption of the result. A group of
                  authorities now makes a threshold decryption of this
                  ciphertext to get the result. We have to protect
                  against voters that cheat by encrypting something
                  that is not a valid vote. We therefore require that
                  they make a non-interactive zero-knowledge argument
                  of correctness of the encrypted vote. Using
                  integer-commitments, we suggest efficient honest
                  verifier zero-knowledge arguments for correctness of
                  a vote, which can be made non-interactive using the
                  Fiat-Shamir heuristic. We suggest arguments for
                  single-voting, multi-way voting, approval voting and
                  shareholder voting, going from the case where the
                  voter has a single vote to the case where a voter
                  may cast millions of votes at once.\bibpar For
                  anonymization purposes, one can use a mix-net. One
                  way to construct a mix-net is to let a set of mixers
                  take turns in permuting and reencrypting or
                  decrypting the inputs. If at least one of the mixers
                  is honest, the input data and the output data can no
                  longer be linked. For this anonymization guarantee
                  to hold we do need to ensure that all mixers act
                  according to the protocol. For use in reencrypting
                  mix-nets we suggest an honest verifier
                  zero-knowledge argument of a correct reencrypting
                  shuffle that can be used with a large class of
                  homomorphic cryptosystems. For use in decrypting
                  mix-nets, we offer an honest verifier zero-knowledge
                  argument for a decrypting shuffle.\bibpar For any
                  NP-language there exists, based on one-way
                  functions, a 3-move honest verifier zero-knowledge
                  argument. If we pick a suitable hard statement and a
                  suitable 3-move argument for this statement, we can
                  use the protocol as a commitment scheme. A
                  commitment to a message is created by using a
                  special honest verifier zero-knowledge property to
                  simulate an argument with the message as
                  challenge. We suggest picking the statement to be
                  proved in a particular way related to a signature
                  scheme, which is secure against known message
                  attack. This way we can create many commitments that
                  can be trapdoor opened, yet other commitments chosen
                  by an adversary remain binding. This property is
                  known as simulation soundness. Simulation soundness
                  implies non-malleability, so we obtain a
                  non-malleable commitment scheme based on any one-way
                  function. We also obtain efficient non-malleable
                  commitment schemes based on the strong RSA
                  assumption.\bibpar We investigate the use of honest
                  verifier zero-knowledge arguments in signature
                  schemes. By carefully selecting the statement to be
                  proven and finding an efficient protocol, we obtain
                  a group signature scheme that is very efficient and
                  has only weak set-up assumptions. Security is proved
                  in the random oracle model. The group signature
                  scheme can be extended to allow for dynamic join of
                  members, revocation of members and can easily be
                  transformed into a traceable signature scheme. We
                  observe that traceable signatures can be built from
                  one-way functions and non-interactive zero-knowledge
                  arguments, which seems to be weaker than the
                  assumptions needed to build group signatures",
  linkhtmlabs =  "",
  linkps = 	 "",
  linkpdf = 	 ""

  author =	 "Berg, Alex Rune",
  title =	 "Rigidity of Frameworks and Connectivity of Graphs",
  institution =	 brics,
  year =	 2004,
  type =	 ds,
  number =	 "DS-04-2",
  address =	 daimi,
  month =	 jul,
  note =	 "PhD thesis. xii+173~pp",
  comment =	 "Defence: July~7, 2004",
  abstract =	 "This dissertation contains results on three
                  different but connected areas. The first area is on
                  rigidity of frameworks. A framework consists of
                  rigid bars and rotatable joints. A framework is
                  rigid if it has no deformation. A graph is
                  generically rigid if every framework obtained as a
                  'generic embedding' of the graph in the plane is
                  rigid. A graph is redundantly rigid if it is
                  generically rigid after removing an arbitrary
                  edge. A graph $G=(V,E)$ is called a {\bf generic
                  circuit} if $|E|=2|V|-2$ and $G$ is redundantly
                  rigid. The operation {\bf extension} subdivides an
                  edge $uw$ of a graph by a new vertex $v$ and adds a
                  new edge $vz$ for some vertex $z\not=
                  u,w$. R. Connelly conjectured that every
                  $3$-connected generic circuit can be obtained from
                  $K_4$ by a sequence of extensions. We prove this
                  conjecture. All new results presented in this
                  dissertation is joint work with T. Jord\'an. A new
                  and simple algorithm for finding the maximal
                  generically rigid subgraphs of a graph has also been
                  developed. The running time matches that of previous
                  algorithms, namely $O(n^2)$. Furthermore a
                  polynomial algorithm has been found for computing
                  maximal generically uniquely realizable graphs in
                  dimension two (also called globally rigid
                  graphs). The algorithm relies heavily on a result of
                  Jackson and Jord\'an.\bibpar Theorems on detachments
                  in $k$-edge-connected directed graphs and splitting
                  off in directed hypergraphs have been obtained. The
                  work described in this paragraph is also joint with
                  B. Jackson. The splitting off operation in a
                  directed graph replaces an arc $\overrightarrow{su}$
                  and arcs
                  by one directed hyperedge having tail vertices
                  $v_1,\ldots,v_t$ and one head vertex $u$. We present
                  a theorem detaching hyperedges preserving
                  $k$-edge-connectivity of the resulting directed
                  hypergraph (for an appropriate definition of
                  $k$-edge-connectivity). The detachment operation in
                  a directed graph 'detaches' a vertex $s$ into
                  several vertices ('pieces') $s_1,\ldots,s_t$ and
                  then distributes the arcs of $s$ among the vertices
                  $s_1,\ldots,s_t$ and finally deletes $s$. We present
                  a theorem stating when it is possible to detach a
                  vertex into $r$ pieces preserving
                  $k$-edge-connectivity of the resulting graph. This
                  detachment theorem correspond to a theorem by
                  Nash-Williams on undirected graphs.\bibpar
                  Orientation results preserving $k$-edge-connectivity
                  have been developed by Nash-Williams. Frank
                  conjectured that a graph $G=(V,E)$, $|V| \geq k+1$,
                  has a $k$-vertex-connected orientation if and only
                  if $G-X$ is $(2k-2|X|)$-edge-connected for all $X
                  \subseteq V$ with $|X| \leq k-1$. Gerards verified
                  Frank's conjecture graphs $G$ where every vertex has
                  degree four and with $k=2$. In this dissertation
                  Frank's conjecture is verified for the Eulerian
                  graphs and still with $k=2$. An algorithm is
                  presented for finding $2$-vertex-connected
                  orientations of Eulerian graphs satisfying Frank's
                  conjecture for $k=2$"

  author = 	 "Klin, Bartosz",
  title = 	 "An Abstract Coalgebraic Approach to Process
                  Equivalence for Well-Behaved Operational
  institution =  brics,
  year = 	 2004,
  type = 	 ds,
  number = 	 "DS-04-1",
  address = 	 daimi,
  month = 	 may,
  note = 	 "PhD thesis. x+152~pp",
  comment = 	 "Defence: May~28, 2004",
  abstract = 	 "This thesis is part of the programme aimed at
                  finding a mathematical theory of well-behaved
                  structural operational semantics. General and
                  basic results shown in 1997 in a seminal paper
                  by Turi and Plotkin are extended in two
                  directions, aiming at greater expressivity of
                  the framework. \bibpar
                  The so-called bialgebraic framework of Turi and
                  Plotkin is an abstract generalization of the
                  well-known structural operational semantics
                  format GSOS, and provides a theory of
                  operational semantic rules for which
                  bisimulation equivalence is a congruence.
                  The first part of this thesis aims at extending
                  that framework to cover other operational
                  equivalences and preorders (e.g.\ trace
                  equivalence), known collectively as the van
                  Glabbeek spectrum. To do this, a novel
                  coalgebraic approach to relations on processes
                  is desirable, since the usual approach to
                  coalgebraic bisimulations as spans of
                  coalgebras does not extend easily to other
                  known equivalences on processes. Such an
                  approach, based on fibrations of test suites,
                  is presented. Based on this, an abstract
                  characterization of congruence formats is
                  given, parametrized by the relation on
                  processes that is expected to be compositional.
                  This abstract characterization is then
                  specialized to the case of trace equivalence,
                  completed trace equivalence and failures
                  equivalence. In the two latter cases, novel
                  congruence formats are obtained, extending the
                  current state of the art in this area of
                  research. \bibpar
                  The second part of the thesis aims at extending
                  the bialgebraic framework to cover a general
                  class of recursive language constructs, defined
                  by (possibly unguarded) recursive equations.
                  Since unguarded equations may be a source of
                  divergence, the entire framework is interpreted
                  in a suitable domain category, instead of the
                  category of sets and functions. It is shown
                  that a class of recursive equations called
                  regular equations can be merged seamlessly with
                  GSOS operational rules, yielding well-behaved
                  operational semantics for languages extended
                  with recursive constructs.",
  linkhtmlabs =  "",
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  linkpdf = 	 ""