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Non-uniform ACC Circuit Lower Bounds
Non-uniform ACC Circuit Lower Bounds   (Citations: 6)
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    • ...recent breakthrough result of Williams [3] who showed that non-deterministic exponential time does not have efficient ACC 0 circuits...

    Arkadev Chattopadhyayet al. Linear Systems over Finite Abelian Groups

    • ...A few months ago, Williams [17] succeeded in carrying out the program by proving an ingenious lower bound for NEXP against non-uniform constant-depth ACC circuits of sub-exponential size (For every fixed depth d, he also provided an exponential-size lower bound), thereby solving a notorious long-standing open problem...
    • ...For more background and history on circuit lower bounds, we refer the readers to [17] which elaborates on this history in detail...
    • ...In [17], Williams gave an algorithm for solving the satisfiability problem of SYM + circuits of size s over n variables in time O((2 n +s)n O(1) ). Combining it with Corollary 1, the following theorem is immediate...
    • ...Note 1. In [17], there are about n δ many input variables set in a single copy...
    • ...In this section, we present our main lower bound result via the framework invented by Williams [17]...
    • ...to note that, because of Theorem 4, it is possible to state a slight variant of Lemma 3.1 of [17]...
    • ...The following theorem is a variant of Theorem 5.2 in [17]...
    • ...the work of Williams [17], our algorithm for deciding the satisfiability of the succinctly represented 3-CNF instance Cx proceeds as the following steps...
    • ...In the recent work by Fortnow and Santhanam [9], they defined notions of robust simulations and significant separations, and showed that the theorem of Williams [17] can be strengthened with respect to significant separations...

    Fengming Wang. NEXP Does Not Have Non-uniform Quasipolynomial-Size ACC Circuits of

    • ...These newer results include hierarchy theorems [Bar02, FS04, vMP06], time-space tradeoffs [For00, FLvMV05], and circuit lower bounds [BFT98, Vin05, San07, Wil10a, Wil10b]...
    • ...Our most technically involved result is that the recent breakthrough lower bound of Williams [Wil10a, Wil10b] can be strengthened to a significant separation...
    • ...Our most technically involved result is that the recent lower bound of Williams [Wil10b] that NEXP � ACC 0 extends to the robustly often setting...
    • ...Now we are ready to prove the robustly often analogue of Williams’ main result [Wil10b]...

    Lance Fortnowet al. Robust Simulations and Significant Separations

    • ...The two topics are time-space lower bounds for the satisfiability problem (originating with work of Fortnow and others [2,3]) and circuit size lower bounds for nondeterministic exponential time [7,8]...

    Ryan Williams. Diagonalization Strikes Back: Some Recent Lower Bounds in Complexity T...

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