First-order queries on structures of bounded degree are computable with constant delay [article]

Arnaud Durand, Etienne Grandjean
2005 arXiv   pre-print
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 first-order 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 , i.e., can be computed by an algorithm that has two separate
more » ... 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(|ϕ|).(||+|ϕ()|)) and space O(f(|ϕ|).||) where is the structure, ϕ is the formula, ϕ() is the result of the query and f is some function. Among other things, our results generalize a result of Seese-96 on the data complexity of the model-checking problem for bounded degree structures. Besides, the originality of our approach compared to that Seese-96 and comparable results is that it does not rely on the Hanf's model-theoretic technic (see Hanf-65) and is completely effective.
arXiv:cs/0507020v1 fatcat:mzjuoylhtrf2nf5upoioy3ono4