We investigate regular realizability (RR) problems, which are the problems of verifying whether the intersection of a regular language – the input of the problem – and a fixed language, called a filter, is nonempty. In this paper we focus on the case of context-free filters. The algorithmic complexity of the RR problem is a very coarse measure of the complexity of context-free languages. This characteristic respects the rational dominance relation. We show that a RR problem for a maximal filter under the rational dominance relation is P-complete. On the other hand, we present an example of a P-complete RR problem for a nonmaximal filter.We show that RR problems for Greibach languages belong to the class NL. We also discuss RR problems with context-free filters that might have intermediate complexity. Possible candidates are the languages with polynomially-bounded rational indices. We show that RR problems for these filters lie in the class NSPACE(log2 n).
CITATION STYLE
Rubtsov, A., & Vyalyi, M. (2015). Regular realizability problems and context-free languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9118, pp. 256–267). Springer Verlag. https://doi.org/10.1007/978-3-319-19225-3_22
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