5,031 research outputs found
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
Desingularization in Computational Applications and Experiments
After briefly recalling some computational aspects of blowing up and of
representation of resolution data common to a wide range of desingularization
algorithms (in the general case as well as in special cases like surfaces or
binomial varieties), we shall proceed to computational applications of
resolution of singularities in singularity theory and algebraic geometry, also
touching on relations to algebraic statistics and machine learning. Namely, we
explain how to compute the intersection form and dual graph of resolution for
surfaces, how to determine discrepancies, the log-canoncial threshold and the
topological Zeta-function on the basis of desingularization data. We shall also
briefly see how resolution data comes into play for Bernstein-Sato polynomials,
and we mention some settings in which desingularization algorithms can be used
for computational experiments. The latter is simply an invitation to the
readers to think themselves about experiments using existing software, whenever
it seems suitable for their own work.Comment: notes of a summer school talk; 16 pages; 1 figur
Dagstuhl News January - December 2007
"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic
Recent progress in exact geometric computation
AbstractComputational geometry has produced an impressive wealth of efficient algorithms. The robust implementation of these algorithms remains a major issue. Among the many proposed approaches for solving numerical non-robustness, Exact Geometric Computation (EGC) has emerged as one of the most successful. This survey describes recent progress in EGC research in three key areas: constructive zero bounds, approximate expression evaluation and numerical filters
Dagstuhl News January - December 2002
"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic
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