Subspace-Invariant AC^0 Formulas
نویسنده
چکیده
The n-variable PARITY function is computable (by a well-known recursive construction) by AC0 formulas of depth d+ 1 and leafsize n·2dn . These formulas are seen to possess a certain symmetry: they are syntactically invariant under the subspace P of even-weight elements in {0, 1}, which acts (as a group) on formulas by toggling negations on input literals. In this paper, we prove a 2d(n−1) lower bound on the size of syntactically P -invariant depth d + 1 formulas for PARITY. Quantitatively, this beats the best 2Ω(d(n−1)) lower bound in the noninvariant setting [16]. 1998 ACM Subject Classification F.1.1 Models of Computation
منابع مشابه
Subspace-Invariant AC Formulas
The n-variable PARITY function is computable (by a well-known recursive construction) by AC formulas of depth d+ 1 and leafsize n·2dn1/d . These formulas are seen to possess a certain symmetry: they are syntactically invariant under the subspace P of even-weight elements in {0, 1}, which acts (as a group) on formulas by toggling negations on input literals. In this paper, we prove a 2 −1) lower...
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