A note on parallel and alternating time |
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Authors: | Felipe Cucker Irne Briquel |
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Institution: | aDepartment of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;bLaboratoire d’Informatique et de Parallélisme, ENS Lyon 46, allée d’Italie, 69364 Lyon Cedex 07, France |
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Abstract: | 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 time is sandwiched between two such classes for different patterns. |
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Keywords: | Complexity classes Parallelism Alternation |
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