Deciding Regular Intersection Emptiness of Complete Problems for PSPACE and the Polynomial Hierarchy
For a regular set R of quantified Boolean formulae we decide whether R contains a true formula. We conclude that there is a PSPACE-complete problem for which emptiness of intersection with a regular set is decidable. Furthermore, by restricting depth and order of quantification we obtain complete problems for each level of the polynomial hierarchy with this decidability as well.
KeywordsAutomata and logic Emptiness of regular intersection Quantified Boolean formula PSPACE Polynomial hierarchy
We thank Benjamin Gras for the fruitful discussions during the TüFTLeR seminar. Also, we give our thanks to Michaël Cadilhac, Silke Czarnetzki and Michael Ludwig for proof-reading.
- 4.Güler, D., Lange, K.J.: What is (Not) a Formal Language (in preparation)Google Scholar
- 9.Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time (preliminary report). In: Proceedings of the Fifth Annual ACM Symposium on Theory of Computing, pp. 1–9. ACM (1973)Google Scholar