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We present a logical approach to complexity over the real numbers with respect to the model of Blum, Shub and Smale. The Iogics under consideration are interpreted over a special class of two-sorted structures, called R-structures They consist of a finite structure together with the ordered field of reals and a finite set of functions from the finite… (More)
In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post's Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only… (More)
In this tutorial paper we overview research being done in the field of structural complexity and recursion theory over the real numbers and other domains following the approach by Blum, Shub, and Smale .
Starting point of our work is a previous paper by Flarup, Koiran, and Lyaudet . There the expressive power of certain families of polynomials is investigated. Among other things it is shown that polynomials arising as permanents of bounded tree-width matrices have the same expressiveness as polynomials given via arithmetic formulas. A natural question is… (More)
BACKGROUND The vascular disrupting agent combretastatin-A4-phosphate (CA4P) demonstrated antitumour activity in preclinical studies when combined with radiation. METHODS Patients with non-small-cell lung cancer (NSCLC), prostate adenocarcinoma, and squamous cell carcinoma of the head and neck (SCCHN) received 27 Gy in 6 fractions treating twice weekly… (More)