Unambiguous Computations and Locally Deenable Acceptance Types

Hertrampf's locally de nable acceptance types show that many complexity classes can be de ned in terms of polynomial time bounded NTM's with simple local conditions on the nodes of its computation tree, rather than global concepts like number of accepting paths etc. We introduce a modi cation of Hertrampf's locally de nable acceptance types which allows to get a larger number of characterizable complexity classes. Among others the newly characterizable classes are UP and ModZkP . It is shown how di erent types of oracle access, e.g., guarded access, can be characterized by this model. This sheds new light on the discussion on how to access unambiguous computation. We present simple functions that describe precisely objects of current research as the unambiguous oracle, alternation, and promise hierarchies. We exhibit the new class UAP which seems to be an unambiguous analogue of Wagner's rP . UAP (and thus rP) contains Few and is currently the smallest class known with this property.