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- W3149509511 abstract "The motivating question for this work is a long standing open problem, posed by Nisan [20], regarding the relative powers of algebraic branching programs (ABPs) and formulas in the non-commutative setting. Even though the general question remains open, we make some progress towards its resolution. To that effect, we generalise the notion of ordered polynomials in the non-commutative setting (defined by Hrubes, Wigderson and Yehudayoff [11]) to define abecedarian polynomials and models that naturally compute them. Our main contribution is a possible new approach towards resolving the VFnc vs VBPnc question, via lower bounds against abecedarian formulas. In particular, we show the following. There is an explicit n2-variate degree d abecedarian polynomial fn,d(x) such that • fn,d(X) can be computed by an abecedarian ABP of size O(nd); • any abecedarian formula computing fn,log n(X) must have size at least nΩ(log log n). We also show that a super-polynomial lower bound against abecedarian formulas for flog n, n(X) would separate the powers of formulas and ABPs in the non-commutative setting." @default.
- W3149509511 created "2021-04-13" @default.
- W3149509511 creator A5053586878 @default.
- W3149509511 date "2021-07-20" @default.
- W3149509511 modified "2023-09-23" @default.
- W3149509511 title "Separating ABPs and some structured formulas in the non-commutative setting" @default.
- W3149509511 doi "https://doi.org/10.4230/lipics.ccc.2021.7" @default.
- W3149509511 hasPublicationYear "2021" @default.
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