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- Paul Beame, Vincent Liew
- UAI
- 2015

We show new limits on the efficiency of using current techniques to make exact probabilis-tic inference for large classes of natural problems. In particular we show new lower bounds on knowledge compilation to SDD and DNNF forms. We give strong lower bounds on the complexity of SDD representations by relating SDD size to best-partition communication… (More)

- Paul Beame, Vincent Liew
- 2017

We eliminate a key roadblock to efficient verification of non-linear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. In particular, we give n O(1) size regular resolution proofs for arbitrary degree… (More)

- Paul Beame, Vincent Liew, Mihai Patrascu
- ICALP
- 2015

We prove that any oblivious algorithm using space S to find the median of a list of n integers from {1,. .. , 2n} requires time Ω(n log log S n). This bound also applies to the problem of determining whether the median is odd or even. It is nearly optimal since Chan, following Munro and Raman, has shown that there is a (randomized) selection algorithm using… (More)

- Vincent Liew
- 2012

In the last lecture we examined relativization. We found that a common method (diagonalization) for proving non-inclusions between classes of problems was, alone, insufficient to settle the P versus N P problem. This was due to the existence of two orcales: one for which P = N P and another for which P = N P. Therefore, in our search for a solution, we must… (More)

- Vincent Liew
- 2012

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