THE DOT-DEPTH AND THE POLYNOMIAL HIERARCHIES CORRESPOND ON THE DELTA LEVELS

BERND BORCHERT, KLAUS-JÖRN LANGE, FRANK STEPHAN, PASCAL TESSON, DENIS THÉRIEN
2005 International Journal of Foundations of Computer Science  
It is well-known that the Σ k -and Π k -levels of the dot-depth hierarchy and the polynomial hierarchy correspond via leaf languages. We extend this correspondence to the ∆ k -levels of these hierarchies: Leaf P (∆ L k ) = ∆ p k . The same methods are used to give evidence against an earlier conjecture of Straubing and Thérien about a leaf-language upper bound for BPP.
doi:10.1142/s0129054105003200 fatcat:ewx73a5ibnhblfrkd776sbq4du