Nondeterminism and An Abstract Formulation of Nečiporuk’s Lower Bound Method

Paul Beame 1 Nathan Grosshans 2, 3 Pierre Mckenzie 2, 3 Luc Segoufin 4, 2
4 DAHU - Verification in databases
LSV - Laboratoire Spécification et Vérification [Cachan], ENS Cachan - École normale supérieure - Cachan, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8643
Abstract : A formulation of Nečiporuk's lower bound method slightly more inclusive than the usual complexity-measure-specific formulation is presented. Using this general formulation, limitations to lower bounds achievable by the method are obtained for several computation models, such as branching programs and Boolean formulas having access to a sublinear number of nondeterministic bits. In particular, it is shown that any lower bound achievable by the method of Nečiporuk for the size of nondeterministic and parity branching programs is at most O(n^(3/2) / log n).
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Paul Beame, Nathan Grosshans, Pierre Mckenzie, Luc Segoufin. Nondeterminism and An Abstract Formulation of Nečiporuk’s Lower Bound Method. ACM Transactions on Computation Theory, ACM, 2016, 9 (1), pp.1 - 34. ⟨10.1145/3013516⟩. ⟨hal-01426213⟩

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