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2004
Springer

Entanglement - A Measure for the Complexity of Directed Graphs with Applications to Logic and Games

10 years 4 months ago
Entanglement - A Measure for the Complexity of Directed Graphs with Applications to Logic and Games
We propose a new parameter for the complexity of finite directed graphs which measures to what extent the cycles of the graph are intertwined. This measure, called entanglement, is defined by way of a game that is somewhat similar in spirit to the robber and cops games used to describe tree width, directed tree width, and hypertree width. Nevertheless, on many classes of graphs, there are significant differences between entanglement and the various incarnations of tree width. Entanglement is intimately connected to the computational and descriptive complexity of the modal µ-calculus. On the one hand, the number of fixed point variables needed to describe a finite graph up to bisimulation is captured by its entanglement. This plays a crucial role in the proof that the variable hierarchy of the µ-calculus is strict. In addition to this, we prove that parity games of bounded entanglement can be solved in polynomial time. Specifically, we establish that the complexity of solving a...
Dietmar Berwanger, Erich Grädel
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Where LPAR
Authors Dietmar Berwanger, Erich Grädel
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