Abstract
Linear-Delay lin is the class of enumeration problems computable in two steps: the first step is a precomputation in linear time in the size of the input and the second step computes successively all the solutions with a delay between two consecutive solutions y 1 and y 2 that is linear in |y 2|. We prove that evaluating a fixed monadic second order (MSO) query \(\varphi(\bar{X})\) (i.e. computing all the tuples that satisfy the MSO formula) in a binary tree is a Linear-Delay lin problem. More precisely, we show that given a binary tree T and a tree automaton Γ representing an MSO query \(\varphi(\bar{X})\), we can evaluate Γ on T with a preprocessing in time and space complexity O(|Γ|3|T|) and an enumeration phase with a delay O(|S|) and space O(max|S|) where |S| is the size of the next solution and max|S| is the size of the largest solution. We introduce a new kind of algorithm with nice complexity properties for some algebraic operations on enumeration problems. In addition, we extend the precomputation (with the same complexity) such that the i th (with respect to a certain order) solution S is produced directly in time O(|S|log(|T|)). Finally, we generalize these results to bounded treewidth structures.
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Bagan, G. (2006). MSO Queries on Tree Decomposable Structures Are Computable with Linear Delay. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_11
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DOI: https://doi.org/10.1007/11874683_11
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