We show that every unary stochastic context-free grammar with polynomially bounded ambiguity, has an equivalent probabilistic automaton.

Abstract In this paper, we present that the propositional proof system R(lin) (Resolution over Linear Equations) established by Ran Raz and Iddo Tzameret is not a super system, there exists a sequence of tautologies, which require proof complexity exponential in size of tautologies. We show that there are the sequence of unsatisfiable collections of disjuncts of linear equations, which require ...

A functional calculus valid for the class of absolutely continuous pairs of commuting polynomially bounded operators is defined.

In this paper we study the metric spaces that are definable in a polynomially bounded ominimal structure. We prove that the family of metric spaces definable in a given polynomially bounded o-minimal structure is characterized by the valuation field Λ of the structure. In the last section we prove that the cardinality of this family is that of Λ. In particular these two results answer a conject...

Consider a 0/1 integer program min{c T x : Ax ≥ b, x ∈ {0, 1} n } where A is nonnegative. We show that if the number of minimal covers of Ax ≥ b is polynomially bounded, then there is a polynomially large relaxation whose value is arbitrarily close to being at least as good as that given by the rank-r closure, for any fixed r. A special case of this result is that given by set-covering problems...

The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...

Consider a 0/1 integer program min{c T x : Ax ≥ b, x ∈ {0, 1} n } where A is nonnegative. We show that if the number of minimal covers of Ax ≥ b is polynomially bounded, then there is a polynomially large lift-and-project relaxation whose value is arbitrarily close to being at least as good as that given by the rank ≤ q cuts, for any fixed q. A special case of this result is that given by set-c...

(1) Many typos have been corrected (2) Some redoundancy has been eliminated Notes on polynomially bounded arithmetic Abstract 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.

It is shown that almost superdiagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces if the nonlocally convex linear topology τ(p i) is locally bounded. 1. Introduction. The purpose of this paper is to show that almost super-diagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces ...