Modal characterisation theorems over special classes of frames
The present investigation primarily concerns ramifications for specific classes of structures defined through conditions on the underlying frames, with a focus on frame classes that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics.
DAG-Width and Parity Games
- Dietmar Berwanger, A. Dawar, P. Hunter, S. Kreutzer
- Mathematics, Computer ScienceSymposium on Theoretical Aspects of Computer…
- 23 February 2006
The natural adaptation of the cops-and-robber game to directed graphs is considered and it is shown 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).
The dag-width of directed graphs
- Dietmar Berwanger, A. Dawar, P. Hunter, S. Kreutzer, J. Obdržálek
- Computer Science, MathematicsJournal of combinatorial theory. Series B (Print)
- 1 July 2012
Affine Systems of Equations and Counting Infinitary Logic
- Albert Atserias, A. Bulatov, A. Dawar
- MathematicsInternational Colloquium on Automata, Languages…
- 9 July 2007
It is shown that testing the solvability of systems of equations over a finite Abelian group, a tractable CSP that was previously known not to be definable in Datalog, is not Definable in an infinitary logic with counting and hence that it is not definite in least fixed point logic or its extension with counting.
Preservation Under Extensions on Well-Behaved Finite Structures
- Albert Atserias, A. Dawar, Martin Grohe
- MathematicsInternational Colloquium on Automata, Languages…
- 11 July 2005
It is shown that the property of extension preservation property holds of classes of acyclic structures, structures of bounded degree and more generally structures that are wide in a sense the authors make precise.
Infinitary Logic and Inductive Definability over Finite Structures
- A. Dawar, S. Lindell, S. Weinstein
- Computer ScienceInformation and Computation
- 1 June 1995
It is shown that a formula of FO + LFP can be written that defines an ordering of the Lk∞?
A Restricted Second Order Logic for Finite Structures
- A. Dawar
- PhilosophyLogical and Computational Complexity
- 13 October 1994
We introduce a restricted version of second order logic SOω in which the second order quantifiers range over relations that are closed under the equivalence relation ≡k of k variable equivalence, for…
Choiceless Polynomial Time, Counting and the Cai-Fürer-Immerman Graphs: (Extended Abstract)
- A. Dawar, David Richerby, Benjamin Rossman
- Computer Science, MathematicsWorkshop on Logic, Language, Information and…
- 1 March 2008
Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree
- Jannis Bulian, A. Dawar
- Mathematics, Computer ScienceAlgorithmica
- 18 June 2014
It is established that graph canonisation, and thus graph isomorphism, is $$\mathsf {FPT}$$FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al.
Parameterized Complexity of First-Order Logic
- S. Kreutzer, A. Dawar
- Mathematics, Computer ScienceElectron. Colloquium Comput. Complex.
- 2009
It is shown that if C is a class of graphs which is nowhere dense then rst-order model-checking is xed-parameter tractable on C, which essentially gives a precise characterisation of classes for which FO model- checking is tractable.
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