Firstorder queries on structures of bounded degree are computable with constant delay
Abstract
A bounded degree structure is either a relational structure all of whose relations are of bounded degree or a functional structure involving bijective functions only. In this paper, we revisit the complexity of the evaluation problem of not necessarily Boolean firstorder queries over structures of bounded degree. Query evaluation is considered here as a dynamical process. We prove that any query on bounded degree structures is $\constantdelaylin$, i.e., can be computed by an algorithm that has two separate parts: it has a precomputation step of linear time in the size of the structure and then, it outputs all tuples one by one with a constant (i.e. depending on the size of the formula only) delay between each. Seen as a global process, this implies that queries on bounded structures can be evaluated in total time $O(f(\phi).(\calS+\phi(\calS)))$ and space $O(f(\phi).\calS)$ where $\calS$ is the structure, $\phi$ is the formula, $\phi(\calS)$ is the result of the query and $f$ is some function. Among other things, our results generalize a result of \cite{Seese96} on the data complexity of the modelchecking problem for bounded degree structures. Besides, the originality of our approach compared to that \cite{Seese96} and comparable results is that it does not rely on the Hanf's modeltheoretic technic (see \cite{Hanf65}) and is completely effective.
 Publication:

arXiv eprints
 Pub Date:
 July 2005
 arXiv:
 arXiv:cs/0507020
 Bibcode:
 2005cs........7020D
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Computational Complexity
 EPrint:
 18 pages, 1 figure