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## On the asymptotic enumeration of accessible automata

## Control and estimation for large-scale systems having spatial symmetry

## Finite-state control of uncertain systems.

## Degree Bounds on Polynomials and Relativization Theory

(a) There is a relativized world where AWPP has no polynomial-time Turing hard set for UP cap coUP. This implies that classes like SPP, LWPP, WPP and AWPP do not possess Turing complete sets robustly; thus we answer an open question of [HRZ95] and extend one of the main results of [HJV93].

(b) There is a relativized world where AWPP has no polynomial-time Turing hard set for ZPP.

(c) There is a relativized world where UP cap coUP is not low for LWPP as well as for WPP. As a consequence, we show that both LWPP and WPP are not uniformly gap-definable. This settles an open question of [FFK94] and gives a relativized answer to another question of [FFK94].

(d) There is a relativized world where NP cap coNP subseteq AWPP.

(e) There is a relativized world where ZPP is not contained in WPP^{WPP}. Thus WPP differs considerably from its superclass C_{=}P, for which it is known that PH subseteq C_{=}P^{C_{=}P} in every relativized world.

(f) Finally, we demonstrate that our proof technique is applicable also to classes that are not known to be gap-definable. We construct a relativized world where MIP cap coMIP has no polynomial-time Turing hard set for ZPP. This extends one of the main results of [HJV93].