This research addresses a high-speed computation method for the Kleene Star of the weighted adjacency matrix in max-plus algebraic system. We focus on systems whose precedence constraints are represented by a directed acyclic graph (DAG), and implement on a Cell Broadband EngineTM (CBE) processor. Using the implementation on a Sony Playstation3TM (PS3) equipped with a CBE processor, we attempt ...

Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the sy...

First we establish a connection between the field of the real numbers and the extended max algebra, based on asymptotic equivalences. Next we propose a further extension of the extended max algebra that will correspond to the field of the complex numbers. Finally we use the analogy between the field of the real numbers and the extended max algebra to define the singular value decomposition of a...

The paper introduces a new approach to define process algebras with quantified transitions. A mathematical model is introduced which allows the definition of various classes of process algebras including the well known models of untimed, probabilistic and stochastic process algebras. For this general mathematical model a bisimulation equivalence is defined and it is shown that the equivalence i...

We extend the hierarchical control method in (Li et al., 2004) to a more generic setting which involves cyclically repeated processes. A hierarchical architecture is presented to facilitate control synthesis. Specifically, a conservative max-plus model for cyclically repeated processes is introduced on the upper level which provides an optimal online plan list. An enhanced min-plus algebra base...

Let a ⊕ b = max(a, b), a ⊗ b = a + b for a, b ∈ R := R ∪ {−∞}. By max-algebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗) extended to matrices and vectors. Max-algebra, which has been studied for more than 40 years, is an attractive way of describing a class of nonlinear problems appearing for instance in machinescheduling, information technology and ...

In this paper we propose an algebra of synchronous scheduling interfaces which combines the expressiveness of Boolean algebra for logical and functional behaviour with the min-max-plus arithmetic for quantifying the non-functional aspects of synchronous interfaces. The interface theory arises from a realisability interpretation of intuitionistic modal logic (also known as Curry-Howard-Isomorphi...

We study the sequence of consecutive powers of a matrix in the max-plus algebra, which has maximum and addition as its basic operations. If the matrix is irreducible then it is well known that the ultimate behavior of the sequence is cyclic. For reducible matrices the ultimate behavior is more complex, but it is also cyclic in nature. We will give a detailed characterization of the rates and pe...

The asymptotic properties of inhomogeneous products in the max-plus algebra context have been investigated. In particular, for products involving matrices with the same unique critical circuit, we have obtained some sufficiency conditions under which the rank of the final product matrix is less than or equal to the length of the critical circuit of the matrices in the product. For a product com...

Various kinds of graph problems, including shortest path computation, proof-number search, dataflow analysis, etc., can be solved by fixed-point computations over functions defined on natural numbers or integers. In this paper, we prove that fixed-point computations are possible for the algebra Z∞ = Z∪{∞,−∞}, which has the operators min, max and plus. Since Z∞ is not well-ordered, we formulate ...