887 research outputs found
On visualisation scaling, subeigenvectors and Kleene stars in max algebra
The purpose of this paper is to investigate the interplay arising between max
algebra, convexity and scaling problems. The latter, which have been studied in
nonnegative matrix theory, are strongly related to max algebra. One problem is
strict visualisation scaling, which means finding, for a given nonnegative
matrix A, a diagonal matrix X such that all elements of X^{-1}AX are less than
or equal to the maximum cycle geometric mean of A, with strict inequality for
the entries which do not lie on critical cycles. In this paper such scalings
are described by means of the max-algebraic subeigenvectors and Kleene stars of
nonnegative matrices as well as by some concepts of convex geometry.Comment: 22 page
*-Continuous Kleene -Algebras for Energy Problems
Energy problems are important in the formal analysis of embedded or
autonomous systems. Using recent results on star-continuous Kleene
omega-algebras, we show here that energy problems can be solved by algebraic
manipulations on the transition matrix of energy automata. To this end, we
prove general results about certain classes of finitely additive functions on
complete lattices which should be of a more general interest.Comment: In Proceedings FICS 2015, arXiv:1509.0282
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