We characterize the collapse of Buss’ bounded arithmetic in terms of the prov­ able collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.

We show that if the Boolean hierarchy collapses to level k, then the polynomial hierarchy collapses to BH3(k), where BH3(k) is the k th level of the Boolean hierarchy over Σ2 . This is an improvement over the known results [3], which show that the polynomial hierarchy would collapse to P [O(log . This result is significant in two ways. First, the theorem says that a deeper collapse of the Boole...

We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that ifPNP[1℄ = PNP[2℄, then the polynomial-time hierarchy collapses to Sp2 p2 \ p2. Even showing that the hierarchy collapsed to p2 remained open prior to this paper.

In [1], Airault, McKean and Moser observed that the motion of poles of a rational solution to the K-dV or Boussinesq equation obeys the Calogero-Moser dynamical system [2, 3, 4] with an extra condition on the configuration of poles. In [8], Krichever observed that the motion of poles of a solution to the KP equation which is rational in t1 obeys the Calogero-Moser dynamical system. In this note...

Educational ergonomics is defined as that field of human factors/ergonomic science concerned with the interaction of educational performance and educational design. The premise of educational ergonomics is that student performance to a substantial degree is context specific---specialized in relation to specific design factors---and that ergonomic interventions directed at design improvements th...