Results 1  10
of
274
Erich Gr"adelAachen University Stephan KreutzerUniversity of Edinburgh
"... Abstract We survey logical formalisms based on inflationary anddeflationary fixed points, and compare them to the (more familiar) logics based on least and greatest fixed points. 1. Dictionary Deflation: reduction in size, importance, or effectiveness;contraction of economic activity resulting in a ..."
Abstract
 Add to MetaCart
Abstract We survey logical formalisms based on inflationary anddeflationary fixed points, and compare them to the (more familiar) logics based on least and greatest fixed points. 1. Dictionary Deflation: reduction in size, importance, or effectiveness;contraction of economic activity resulting in a decline of prices; the erosion of soil by the wind. Depletion: the exhaustion of a principal substance, especially a natural resource; a reduction in number or quantity so as to endanger the ability to function. 2. Introduction Fixed point logics extend a basic logical formalism (likefirstorder logic, conjunctive queries, or propositional modal logic) by constructors for defining fixed points ofrelational operators. The most influential fixed point formalisms in computer science are based on least and greatestfixed points of monotone operators. The modal _calculus L _ is the extension of propositionalmodal logic by least and greatest fixed points. In terms of expressive power, it subsumes a variety of modal and temporal logics used in verification, in particular LTL, CTL, CTL\Lambda, PDL and also many logics from other areas of computer science. On the other hand,
Probabilistic Automata with Parameters
"... I am grateful to my supervisors James Worrell and Joël Ouaknine for the great topic and invaluable guidance, support, discussions and suggestions during my work on the dissertation. I would also like to thank Stephan Kreutzer a lot for guiding me through this master’s program. ..."
Abstract
 Add to MetaCart
I am grateful to my supervisors James Worrell and Joël Ouaknine for the great topic and invaluable guidance, support, discussions and suggestions during my work on the dissertation. I would also like to thank Stephan Kreutzer a lot for guiding me through this master’s program.
The glory of the human spirit is the single purpose of all science.
, 2011
"... As stated by John Donne, “no man is an island, entire of itself”. This fact makes life worth living and is the basis that enables one to write a thesis. There is a large number of people and institutions that I would like to thank. This thesis would not have been possible without them. First of all, ..."
Abstract
 Add to MetaCart
for having worked together with Stefan Göller, Stephan Kreutzer, Jens Lehmann and Matthew Parkinson. Moreover, I would like to thank Byron Cook and Samin Ishtiaq for my stay and the work we did at Microsoft Research Cambridge. I am also grateful for inspiring lab discussions I had with Vidjay D
DAGwidth and parity games
 IN PROCEEDINGS OF THE 23RD ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS
, 2006
"... Treewidth is a wellknown metric on undirected graphs that measures how treelike a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Treewidth is characterised by a game known as the copsandrobber game where a number of cops chase a robber on the gr ..."
Abstract

Cited by 56 (9 self)
 Add to MetaCart
Treewidth is a wellknown metric on undirected graphs that measures how treelike a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Treewidth is characterised by a game known as the copsandrobber game where a number of cops chase a robber on the graph. We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure with an associated notion of graph decomposition that can be seen to describe how close a directed graph is to a directed acyclic graph (DAG). This promises to be useful in developing algorithms on directed graphs. In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded DAGwidth. We also consider the relationship between DAGwidth and other measures of such as entanglement and directed treewidth. One consequence we obtain is that certain NPcomplete problems such as Hamiltonicity and disjoint paths are polynomialtime computable on graphs of bounded DAGwidth.
Algorithmic MetaTheorems
 In M. Grohe and R. Neidermeier eds, International Workshop on Parameterized and Exact Computation (IWPEC), volume 5018 of LNCS
, 2008
"... Algorithmic metatheorems are algorithmic results that apply to a whole range of problems, instead of addressing just one specific problem. This kind of theorems are often stated relative to a certain class of graphs, so the general form of a meta theorem reads “every problem in a certain class C of ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
Algorithmic metatheorems are algorithmic results that apply to a whole range of problems, instead of addressing just one specific problem. This kind of theorems are often stated relative to a certain class of graphs, so the general form of a meta theorem reads “every problem in a certain class C of problems can be solved efficiently on every graph satisfying a certain property P”. A particularly well known example of a metatheorem is Courcelle’s theorem that every decision problem definable in monadic secondorder logic (MSO) can be decided in linear time on any class of graphs of bounded treewidth [1]. The class C of problems can be defined in a number of different ways. One option is to state combinatorial or algorithmic criteria of problems in C. For instance, Demaine, Hajiaghayi and Kawarabayashi [5] showed that every minimisation problem that can be solved efficiently on graph classes of bounded treewidth and for which approximate solutions can be computed efficiently from solutions of certain subinstances, have a PTAS on any class of graphs excluding a fixed minor. While this gives a strong unifying explanation for PTAS of many
Digraph measures: Kelly decompositions, games and orderings
"... We consider various wellknown, equivalent complexity measures for graphs such as elimination orderings, ktrees and cops and robber games and study their natural translations to digraphs. We show that on digraphs all these measures are also equivalent and induce a natural connectivity measure. We i ..."
Abstract

Cited by 36 (5 self)
 Add to MetaCart
We consider various wellknown, equivalent complexity measures for graphs such as elimination orderings, ktrees and cops and robber games and study their natural translations to digraphs. We show that on digraphs all these measures are also equivalent and induce a natural connectivity measure. We introduce a decomposition for digraphs and an associated width, Kellywidth, which is equivalent to the aforementioned measure. We demonstrate its usefulness by exhibiting a number of potential applications including polynomialtime algorithms for NPcomplete problems on graphs of bounded Kellywidth, and complexity analysis of asymmetric matrix factorization. Finally, we compare the new width to other known decompositions of digraphs.
ACADEMIC AWARDS AND ACHIEVEMENTS
, 1997
"... Currently employed as a postdoctoral researcher in the Département d’Informatique, Universite ́ Libre de Bruxelles (ULB) in the inVEST project under JeanFrançois Raskin. ..."
Abstract
 Add to MetaCart
Currently employed as a postdoctoral researcher in the Département d’Informatique, Universite ́ Libre de Bruxelles (ULB) in the inVEST project under JeanFrançois Raskin.
Model Theoretic Methods in Finite Combinatorics
, 2009
"... Purpose of the special session We want to bring the various aspects of the interaction between Model Theory and Finite Combinatorics to a wider audience. Altough the work on 01 laws is by now widely known, the other applications on counting functions, graph polynomials, extremal combinatorics, grap ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Purpose of the special session We want to bring the various aspects of the interaction between Model Theory and Finite Combinatorics to a wider audience. Altough the work on 01 laws is by now widely known, the other applications on counting functions, graph polynomials, extremal combinatorics, graph minors and regularity lemmas, have not yet received their deserved attention. Background In the last twenty years several applications of Logic, in particular Model theory, to problems in Combinatorics emerged. Among them we have • 01 laws and their variations. This is well summarized in the book by J. Spencer [Spe01]. • Modular linear recurrence relations for combinatorial counting functions (The SpeckerBlatter Theorem) This theorem has remained widely unnoticed, and deserves wider attention and further study [Spe88, Fis03, FM03]
Inflationary Fixed Points in Modal Logic
, 2002
"... We consider an extension of modal logic with an operator for constructing... ..."
Abstract

Cited by 26 (9 self)
 Add to MetaCart
We consider an extension of modal logic with an operator for constructing...
Results 1  10
of
274