Gap-deenability as a Closure Property ?
نویسندگان
چکیده
Gap-deenability and the gap-closure operator were deened in FFK91]. Few complexity classes were known at that time to be gap-deenable. In this paper, we give simple characterizations of both gap-deenability and the gap-closure operator, and we show that many complexity classes are gap-deenable, including P #P , P #P1] , PSPACE, EXP, NEXP, MP, and BP P. If a class is closed under union, intersection and contains ; and , then it is gap-deenable if and only if it contains SPP; its gap-closure is the closure of this class together with SPP under union and intersection. On the other hand, we give some examples of classes which are reasonable gap-deenable but not closed under union (resp. intersection, complement). Finally, we show that a complexity class such as PP or PSPACE, if it is not equal to SPP, contains a maximal proper gap-deenable subclass which is closed under many-one reductions.
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