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An active line of research in proof complexity over the last decade has been the study of proof space and trade-offs between size and space. Such questions were originally motivated by practical SAT solving, but have also led to the development of new theoretical concepts in proof complexity of intrinsic interest and to results establishing nontrivial… (More)

We present a general method for converting any family of unsatisfiable CNF formulas that is hard for one of the simplest proof systems -- tree resolution -- into formulas that require large rank in very strong proof systems, including any proof system that manipulates polynomials of degree at most k (known as Th(k) proofs). These include high degree… (More)

We consider the read/write streams model, an extension of the standard data stream model in which an algorithm can create and manipulate multiple read/write streams in addition to its input data stream. Like the data stream model, the most important parameter for this model is the amount of internal memory used by such an algorithm. The other key parameters… (More)

- PAUL BEAME, TRINH HUYNH
- 2008

We prove an n Ω(1) /4 k lower bound on the randomized k-party communication complexity of depth 4 AC 0 functions in the number-on-forehead (NOF) model for up to Θ(log n) players. These are the first non-trivial lower bounds for general NOF multiparty communication complexity for any AC 0 function for ω(log log n) players. For non-constant k the bounds are… (More)

We prove an n Ω(1) /4 k lower bound on the randomized k-party communication complexity of depth 4 AC 0 functions in the number-on-forehead (NOF) model for up to Θ(log n) players. These are the first nontrivial lower bounds for general NOF multiparty communication complexity for any AC 0 function for ω(log log n) players. For nonconstant k the bounds are… (More)

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