Singular value automata and approximate minimization

The present paper uses spectral theory of linear operators to construct approximatelyminimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the singular value decomposition (SVD) decomposition of finite-rank infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankelmatrix, and (iii) an algorithmto construct approximateminimizations of given weighted automata by truncating the canonical form.We give bounds on the quality of our approximation.

Design of Fused-Deposition ABS Components for Stiffness and Strength

The high degree of automation of Solid Freeform Fabrication (SFF) processing and its ability to create geometrically complex parts to precise dimensions provide it with a unique potential for low volume production of rapid tooling and functional components. A factor of significant importance in the above applications is the capability of producing components with adequate mechanical performance (e.g., stiffness and strength). This paper introduces a strategy for optimizing the design of Fused-Deposition Acrylonitrile-Butadiene-Styrene (FD-ABS; P400) components for stiffness and strength under a given set of loading conditions. In this strategy, a mathematical model of the structural system is linked to an approximate minimization algorithm to find the settings of select manufacturing parameters, which optimize the mechanical performance of the component. The methodology is demonstrated by maximizing the load carrying capacity of a two-section cantilevered FD-ABS beam.