32774959
Reachability and Invariance Problems in Max-plus Algebra
We present a synthesis of recent results concerning reachability and invariance problems for max-plus linear dynamical systems. Semigroup membership and orbit problems, reachable spaces, and A, B invariant spaces, are discussed.
10167406
Reachability Problems for Products of Matrices in Semirings
We consider the following matrix reachability problem: given r square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? Similarly, we define the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied on the left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any r ≥ 2 is equivalent to the specialization to r = 2. As an application of these reductions and of a theorem of Krob, we show that when r = 2, the vector and matrix reachability problems are undecidable over the max-plus semiring (ℤ∪{-∞}, max,+). These reductions also improve known results concerning the classical zero corner problem. Finally, we show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are "positive", like the tropical semiring (ℤ∪{+∞}, min,+).
62560157
A Version Server for Computer-Aided Design Data
A design database organizes the description of an artifact, by arranging it as a hierarchical composition of components across multiple representations. It is particularly difficult to manage this complex structure as it evolves over time . In this paper, we present a logical organization for describing designs across time. We also present an operational model, based on workspaces and transactions, that describes how these structures can be manipulated while controlling the sharing and integrity of the design database. These concepts are being implemented in a Version Server under development at the University of California, Berkeley.
1662504
The Case for Design Using the World Wide Web
Most information and services required today by designers will soon become available as documents distributed in a wide area hypermedia network. New integration services are required from the design environment, supporting business transactions with design information providers, automatic exchange of design data between independent groups, and integrated support for new forms of collaboration. We discuss design using electronic commerce and other services based on the Internet, and propose a hypermedia system organization for a new generation of CAD systems, conceived to make efficient use of that infrastructure. We also describe our experience as designers of an integrated design and documentation system that interfaces existing design and documentation tools with electronic commerce services based on the World Wide Web.