We show that the answer to the Burnside problem is positive for semigroups of matrices with entries in the (max;+)-algebra (that is, the semiring (R[ f 1g;max;+)), and also for semigroups of (max;+)-linear projective maps with rational entries. An application to the estimation of the Lyapunov exponent of certain products of random matrices is also discussed. Key-words: Semigroups, Burnside Prob...

In this paper, we deene a max-plus algebra of signals for the evaluation of timing behavior of discrete event systems modeled by timed event graphs. We restrict ourselves to innnite, periodic sequences for which we can compute nite representations called signals. This framework allows us to implement a max-plus algebra for computing supremal controllers for real-time, discrete event systems.

We present an extended version of max-plus algebra which includes the inverse operator of “max”. This algebra enables us to ultra-discretize the system including subtractions and obtain new ultra-discrete equations. The known ultra-discrete equations can also be recovered by this construction. PACS numbers: 02.30.Ik, 02.30.Jr, 05.45.Yv

Let a⊕b = max(a, b) and a⊗b = a+b for a, b ∈ R. Max-algebra is an analogue of linear algebra developed on the pair of operations (⊕,⊗) extended to matrices and vectors. The system of equations A ⊗ x = b and inequalities C ⊗ x ≤ d have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We...