2009 50th Annual IEEE Symposium on Foundations ofâ€¦

2009

Toda \cite{Toda} proved in 1989 that the (discrete) polynomial time hierarchy,$\mathbf{PH}$, is contained in the class $\mathbf{P}^{\#\mathbf{P}}$, namely the class of languages that can be decidedâ€¦ (More)

A theorem by Wilkie says that the structure generated by Pfaffian functions is o-minimal. In order to be able to give quantitative version of this result, Gabrielov was lead to introduce the notionâ€¦ (More)

Let A âŠ† R be a set definable in an o-minimal expansion S of the real field, Aâ€² âŠ† R be its projection, and assume that the non-empty fibers Aa âŠ† R n are compact for all a âˆˆ Aâ€² and uniformly bounded,â€¦ (More)

Let S âŠ‚ Rk+m be a compact semi-algebraic set defined by P1 â‰¥ 0, . . . , Pl â‰¥ 0, where Pi âˆˆ R[X1, . . . , Xk , Y1, . . . , Ym], and deg(Pi) â‰¤ 2, 1 â‰¤ i â‰¤ l. Let Ï€ denote the standard projection fromâ€¦ (More)

Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskiiâ€™s Pfaffian functions. In this paper, we useâ€¦ (More)

Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskiiâ€™s Pfaffian functions. In this paper, we useâ€¦ (More)

Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskiiâ€™s Pfaffian functions. In this paper, use theâ€¦ (More)

The notion of (k, m)-agreeable society was introduced by Deborah Berg et al.:a family of convex subsets of R is called (k, m)-agreeable if any subfamily of size m contains at least one non-emptyâ€¦ (More)