A note on parallel and alternating time

Felipe Cucker, Irénée Briquel
2007 Journal of Complexity  
A long standing open question in complexity theory over the reals is the relationship between parallel time and quantifier alternation. It is known that alternating digital quantifiers is weaker than parallel time, which in turn is weaker than alternating unrestricted (real) quantifiers. In this note we consider some complexity classes defined through alternation of mixed digital and unrestricted quantifiers in different patterns. We show that the class of sets decided in parallel polynomial
more » ... e is sandwiched between two such classes for different patterns.
doi:10.1016/j.jco.2007.02.005 fatcat:ik3fywqtrbfo7kpqygzxgpwcnm