Notions of unambiguity for uniform circuits and AuxPDAs are studied and related to each other. In particular, a coincidence for counting and unambiguous versions of AuxPDAs and semi-unbounded fan-in circuits is shown. Moreover, an improved simulation of LOGUCFL (the class of languages logspace many-one reducible to unambiguous context-free languages) by unambiguous circuits and AuxPDAs is devel...

Abstract We consider a special case of the outer bi-Lipschitz classification real semialgebraic (or, more general, definable in polynomially bounded o-minimal structure) surface germs, obtained as union two normally embedded Hölder triangles. define combinatorial invariant an equivalence class such called $$\sigma \tau $$ <mml...

We want to compute a worst case ε-approximation to the solution of the Helmholtz equation −1u+qu = f over the unit d-cube Id , subject to Neumann boundary conditions ∂νu = g on ∂Id . Let card(ε, d) denote the minimal number of evaluations of f , g, and q needed to compute an absolute or normalized ε-approximation, assuming that f , g, and q vary over balls of weighted reproducing kernel Hilbert...

A b s t r a c t. Polysplines on strips of order p are natural generalizations of univariate splines. In [3] and [4] interpolation results for cardinal polysplines on strips have been proven. In this paper the following problems will be addressed: (i) positivity of the fundamental polyspline on the strip [−1, 1] × Rn, and (ii) uniqueness of interpolation for polynomially bounded cardinal polyspl...

Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border between (strongly) NP-hard and polynomially solvable cases of the ...

Definition 1. Let {Xn}, {Yn} be sequences of distributions withXn, Yn ranging over {0, 1}`(n) for some `(n) = nO(1). {Xn} and {Yn} are computationally indistinguishable (notation: Xn ≈ Yn) if for every polynomial-time A and polynomially-bounded , and sufficiently large n ∣∣Pr[A(Xn) = 1]− Pr[A(Yn) = 1]∣∣ ≤ (n) (If we want to nitpick, we’d give 1n as additional input to A to ensure it can run in ...

A language L is called thin if there exists an integer n0 such that for all n n0 L contains at most one word of length n. We show that thinness is decidable for exponential D0L languages. We show also that Siegel's result concerning integral points on algebraic curves of positive genus can often be used to prove that a polynomially bounded HD0L language is thin. TUCS Research Group Mathematical...

We provide a method that approximates the Bayes error rate and the Shannon entropy with high probability. The Bayes error rate approximation makes possible to build a classifier that polynomially approaches Bayes error rate. The Shannon entropy approximation provides provable performance guarantees for learning trees and Bayesian networks from continuous variables. Our results rely on some reas...

Computing the maximal bicliques of a bipartite graph is equivalent to generating the concepts of the binary relation defined by the matrix of this graph. We study this problem for special classes of input relations for which concepts can be generated much more efficiently than in the general case; in some special cases, we can even say that the number of concepts is polynomially bounded, and al...

We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails. Spins are unbounded. The interactions are bounded and finite range. The self potential enters into two classes of measures, κ-concave probability measure and sub-exponential laws, for which it is known that no exponential decay can occur. We prove, using coercive inequalities, that the associated infinite v...