We prove that weakly o-minimal expansions of the ordered field of all real algebraic numbers are polynomially bounded. Apart of this we make a couple of observations concerning weakly o-minimal expansions of ordered fields of finite transcendence degree over the rationals. We show for instance that if Schanuel’s conjecture is true and K ⊆ R is a field of finite transcendence degree over the rat...

We introduce a protocol for authentication between a human and a computer, where the human is able to use no special hardware other than a dumb terminal. Authentication is based on a shared secret which can be reused polynomially often with no danger of exposure, assuming the conjectured uniform hardness of learning parity functions in the presence of noise. Under this conjecture, the protocol ...

Based on several scheduling examples some classes of polynomially solvable sequencing problems with and without precedence constraints are considered. Suucient conditions for the existence of an adjacent pair interchange (API)-relation are derived in the case of sum-and bottleneck-objective functions. Furthermore, we obtain new conditions which are necessary and suucient for the optimality of p...

We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a polynomially bounded o-minimal structure over the reals, surface germs. In particular, any Hölder triangle is either normally embedded or contains some “abnormal” arcs. show that abnormal arcs constitute finitely many “abnormal zones” space all arcs, and investigate geometric combinatorial properties establ...

A condition is identified that implies solutions to the stochastic reaction-diffusion equation ?u ?t=Au+f(u)+?(u)W? on a bounded spatial domain never explode. We consider case where ? grows polynomially and f dissipative, meaning strongly forces toward finite values. This result demonstrates role deterministic forcing term plays in preventing explosion.

In this paper, variety means a class of similar algebras—i.e., models of one firstorder language without relation symbols—which is defined by the satisfaction of some fixed sets of equations. A variety is locally finite if all of its finitely generated members are finite. Following J. Berman and P. Idziak [2], the G-spectrum, or generative complexity, of a locally finite variety C, is the funct...

Tree-width and clique-width are two important graph complexity measures that serve as parameters in many fixed-parameter tractable (FPT) algorithms. The same classes of sparse graphs, in particular of planar graphs and of graphs of bounded degree have bounded tree-width and bounded clique-width. We prove that, for sparse graphs, clique-width is polynomially bounded in terms of tree-width. For p...

We prove an analog of Parikh’s theorem for weighted context-free grammars over commutative, idempotent semirings, and exhibit a stochastic context-free grammar with behavior that cannot be realized by any stochastic right-linear context-free grammar. Finally, we show that every unary stochastic context-free grammar with polynomially-bounded ambiguity has an equivalent stochastic right-linear co...