Years and Authors of Summarized Original Work
2012, 2013; Courcelle, Durand
Problem Definition
The verification of monadic second-order (MSO) graph properties, equivalently, the model-checking problem for MSO logic over finite binary relational structures, is fixed-parameter tractable (FPT) where the parameter consists of the formula that expresses the property and the tree-width or the clique-width of the input graph or structure. How to build usable algorithms for this problem? The proof of the general theorem (an algorithmic meta-theorem, cf. [12]) is based on the description of the input by algebraic terms and the construction of finite automata that accept the terms describing the satisfying inputs. But these automata are in practice much too large to be constructed [11, 14]. A typical number of states is \(2^{2^{10} }\), and lower bounds match this number. Can one use automata and overcome this difficulty?
Key Results
We propose to use fly-automata (FA) [3]. They are automata...
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Recommended Reading
Comon H. et al (2007) Tree automata techniques and applications. http://tata.gforge.inria.fr/
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Courcelle, B., Durand, I. (2016). Model Checking with Fly-Automata. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_692
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