Automata for the verification of monadic second-order graph properties

Implementation and Application of Automata

Durand

2011

Self Cite

Abstract. We address the concrete problem of implementing huge bottom-up term automata. Such automata arise from the verification of Monadic Second Order propositions on graphs of bounded tree-width or clique-width. This applies to graphs of bounded tree-width because bounded tree-width implies bounded clique-width. An automaton which has so many transitions that they cannot be stored in a transition table is represented be a fly-automaton in which the transition function is represented by a finite set of meta-rules. Fly-automata have been implemented inside the Autowrite 1 software and experiments have been run in the domain of graph model checking 2 .

Section: Methodsmentioning

confidence: 99%

Section: Graphs As Logical Structuresmentioning

confidence: 99%

Fly-Automata, Their Properties and Applications

Implementation and Application of Automata

Durand

2011

Self Cite

“…(We will not manipulate tree-decompositions.) We denote by twd(G) the tree-width of a graph G. Similarly, for clique-width 9 , denoted by cwd(G), we refer the reader to [12,15,16,17,18,19].…”

Section: Tree-width and Clique-widthmentioning

confidence: 99%

“…They form a class of bounded expansion (Propo-sition 2.11). A 1-planar graph has at most 4n − 8 edges for n vertices, and 1-planarity is an NP-complete property 16 [11,20]. The class of p-quasi-planar graphs, studied in [1,27,28], is QP (N p+1 ).…”

Section: Graph Property Some Crossing Graph Has: Planaritymentioning

confidence: 99%

On quasi-planar graphs: Clique-width and logical description

Discrete Applied Mathematics

2020

Self Cite

Motivated by the construction of FPT graph algorithms parameterized by clique-width or tree-width, we study graph classes for which treewidth and clique-width are linearly related. This is the case for all graph classes of bounded expansion, but in view of concrete applications, we want to have "small" constants in the comparisons between these width parameters.We focus our attention on graphs that can be drawn in the plane with limited edge crossings, for an example, at most p crossings for each edge. These graphs are called p-planar. We consider a more general situation where the graph of edge crossings must belong to a fixed class of graphs D. For p-planar graphs, D is the class of graphs of degree at most p. We prove that tree-width and clique-width are linearly related for graphs drawable with a graph of crossings of bounded average degree.We prove that the class of 1-planar graphs, although conceptually close to that of planar graphs, is not characterized by a monadic second-order sentence. We identify two subclasses that are.

“…However, these automata have in most cases so many states that their transition tables cannot be built [13,15]. In the article [4] we have introduced automata called fly-automata whose states are described (but not listed) and whose transitions are computed on the fly (and not tabulated). Fly-automata can have infinite sets of states.…”

Section: Introductionmentioning

confidence: 99%

Model-Checking by Infinite Fly-Automata

Durand

2013

Algebraic Informatics

Self Cite

Abstract. We present logic based methods for constructing XP and FPT graph algorithms, parameterized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make it possible to check properties that are not monadic second-order expressible because their states may include counters, so that their set of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. We present tools for constructing easily algorithms by combining predefined automata for basic functions and properties.