6,045 research outputs found
On Integer Images of Max-plus Linear Mappings
Let us extend the pair of operations (max,+) over real numbers to matrices in
the same way as in conventional linear algebra. We study integer images of
max-plus linear mappings. The question whether Ax (in the max-plus algebra) is
an integer vector for at least one x has been studied for some time but
polynomial solution methods seem to exist only in special cases. In the
terminology of combinatorial matrix theory this question reads: is it possible
to add constants to the columns of a given matrix so that all row maxima are
integer? This problem has been motivated by attempts to solve a class of
job-scheduling problems. We present two polynomially solvable special cases
aiming to move closer to a polynomial solution method in the general case
Fejer and Suffridge polynomials in the delayed feedback control theory
A remarkable connection between optimal delayed feedback control (DFC) and
complex polynomial mappings of the unit disc is established. The explicit form
of extremal polynomials turns out to be related with the Fejer polynomials. The
constructed DFC can be used to stabilize cycles of one-dimensional non-linear
discrete systems
Rigidity of critical circle mappings, I
We prove that two critical circle maps with the same rotation number of
bounded type are conjugate for some provided their
successive renormalizations converge together at an exponential rate in the
sense. The number depends only on the rate of convergence. We
also give examples of critical circle maps with the same rotation
number that are not conjugate for any
Underapproximation of Procedure Summaries for Integer Programs
We show how to underapproximate the procedure summaries of recursive programs
over the integers using off-the-shelf analyzers for non-recursive programs. The
novelty of our approach is that the non-recursive program we compute may
capture unboundedly many behaviors of the original recursive program for which
stack usage cannot be bounded. Moreover, we identify a class of recursive
programs on which our method terminates and returns the precise summary
relations without underapproximation. Doing so, we generalize a similar result
for non-recursive programs to the recursive case. Finally, we present
experimental results of an implementation of our method applied on a number of
examples.Comment: 35 pages, 3 figures (this report supersedes the STTT version which in
turn supersedes the TACAS'13 version
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