18,854 research outputs found
Sigref ā A Symbolic Bisimulation Tool Box
We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation.
We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center āAutomatic Verification and Analysis of Complex Systemsā (SFB/TR 14 AVACS). See www.avacs.org for more information
Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Singularities
This paper considers the optimization problem of minimizing a rational
function. We reformulate this problem as polynomial optimization by the
technique of homogenization. These two problems are shown to be equivalent
under some generic conditions. The exact Jacobian SDP relaxation method
proposed by Nie is used to solve the resulting polynomial optimization. We also
prove that the assumption of nonsingularity in Nie's method can be weakened as
the finiteness of singularities. Some numerical examples are given to
illustrate the efficiency of our method.Comment: 23 page
Design automation with the characteristics properties model and the property driven design for redesign
This paper presents a framework consisting of a mathematical model and an algorithm for representation, analysis and exploration of the design space in redesign problems. The framework develops and extends the existing formalism of the Characteristics Properties Model (CPM) and Property Driven Design (PDD). A platform independent quantitative model based on formal log-ic is presented to map the characteristics and properties, as well as the relations and dependencies between them, along with solution conditions. The model is based on generalization of existing mathematical design models and is support-ed by the development of an algorithm enabling property driven design. The re-sulting framework offers a rich and flexible syntax and vocabulary along with a mathematical and computational tool applicable to mechanical product design
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