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The exact complexity of the weak pigeonhole principle is an old and fundamental problem in proof complexity. Using a diagonalization argument, Paris, Wilkie and Woods 16] showed how to prove the weak pigeonhole principle with bounded-depth, quasipolynomial-size proofs. Their argument was further reened by Kraj cek 9]. In this paper, we present a new proof:(More)
It is known that constant-depth Frege proofs of some tautologies require exponential size. No such lower bound result is known for more general proof systems. We consider sequent calculus proofs in which formulas can contain modular connectives and only the cut formulas are restricted to be of constant depth. Under a plausible hardness assumption concerning(More)
In this paper, we show how to extend the argument due to Bonet, Pitassi and Raz to show that bounded-depth Frege proofs do not have feasible interpolation, assuming that factoring of Blum integers or computing the Diffie-Hellman function is sufficiently hard. It follows as a corollary that bounded-depth Frege is not automatizable; in other words, there is(More)
The notion of a p-variety arises in the algebraic approach to Boolean circuit complexity. It has great signi cance, since many known and conjectured lower bounds on circuits are equivalent to the assertion that certain classes of semigroups form p-varieties. In this paper, we prove that semigroups of dot-depth one form a p-variety. This example has the(More)
We investigate the complexity of depth-3 threshold circuits with majority gates at the output, possibly negated AND gates at level two, and MOD m gates at level one. We show that the fan-in of the AND gates can be reduced to O(log n) in the case where m is unbounded, and to a constant in the case where m is constant. We then use these upper bounds to derive(More)
We search for the technicolor process pp-->rhoT/omegaT-->WpiT in events containing one electron and two jets, in data corresponding to an integrated luminosity of 390 pb(-1), recorded by the D0 experiment at the Fermilab Tevatron. Technicolor predicts that technipions pi(T) decay dominantly into bb, bc, or bc, depending on their charge. In these events b(More)
Anomalous Wtb couplings modify the angular correlations of the top-quark decay products and change the single top-quark production cross section. We present limits on anomalous top-quark couplings by combining information from W boson helicity measurements in top-quark decays and anomalous coupling searches in the single top-quark final state. We set limits(More)
Constant-depth polynomial-size threshold circuits are usually classiied according to their total depth. For example, the best known threshold circuits for iterated multiplication and division have depth four and three, respectively. In this paper, the complexity of threshold circuits is investigated from a diierent point of view: explicit AND, OR gates are(More)
In a data sample of approximately 1.3 fb;{-1} collected with the D0 detector between 2002 and 2006, the orbitally excited charm state D_{s1};{+/-}(2536) has been observed with a measured mass of 2535.7+/-0.6(stat)+/-0.5(syst) MeV/c;{2} via the decay mode B_{s};{0}-->D_{s1};{-}(2536)mu;{+}nu_{mu}X. A first measurement is made of the branching ratio product(More)