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...

farabi has simultaniously deep philosopical debates and very clear literature in the area of political sciology. he analyses society as hierarchy. the features of temper and psychological and capabilities have been affected by that hierarchy which is desinged and leept by political leaders. therefore rule, leadership and politics are important from farabi`s view. but at the same time education ...

We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales.

Hierarchical Structures So far, we have studied sequential structures which assigns each of their elements an index in the structure. This imposes an ordering relationship between elements based on this index. Now we will examine more complex relationships that we can impose between elements in a structure. The first of these is the hierarchy which establishes child-parent relationships between...

and identify the essential concepts Arrange all concepts according different weight values Identification root concepts Define preference concept ontology relations in the hierarchy Identify different word morphs, abbreviation, synonyms, etc. Collect preference concept terms Evaluate accuracy against Preference ontology generation Empirical study Design

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...

We present a dialogue system that interprets short questions and short answers within a typed feature structure grammar with a multidimensional construction hierarchy. The system provides a procedure for computing the content values of clausal fragments from contextual information contained in a discourse record of previously processed sentences. The feature system we use is based on an indepen...

A definition of nonstandard universe which gets over the limitation to the finite levels of the cumulative hierarchy is proposed. Though necessarily nonwellfounded, nonstandard universes are arranged in strata in the likeness of superstructures and allow a rank function taking linearly ordered values. Nonstandard universes are also constructed which model the whole ZFC theory without regularity...

Qualitative variables take symbolic values, such as hot, shoe, Europe or France. Sometimes, the values may be arranged in layers or levels of detail. For instance, the variable place_of_origin takes as level-1 values European, African... as level-2 values French, German... as level-3 values Californian, Texan... The paper describes a hierarchy, a mathematical construct among these variables. Th...