Abstract. Given any complex Laurent polynomial f , Amoeba(f ) is the image of its complex zero set under the coordinate-wise log absolute value map. We give an efficiently constructible polyhedral approximation, ArchTrop(f ), of Amoeba(f ), and derive explicit upper and lower bounds, solely as a function of the number of monomial terms of f , for the Hausdorff distance between these two sets. We also show that deciding whether a given point lies in ArchTrop(f ) is doable in polynomial-time, for any fixed dimension, unlike the corresponding problem for Amoeba(f ), which is NP-hard already in one variable. ArchTrop(f ) can thus serve as a canonical low order approximation to start any higher order iterative polynomial system solving algorithm, such as homotopy continuation. ArchTrop(f ) also provides an Archimedean analogue of Kapranov's Non-Archimedean Amoeba Theorem and a higher-dimensional extension of earlier estimates of Mikhalkin and Ostrowski.In memory of Mikael Passare.
We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singular relative to the Markov measure. Also, we determine statistical properties of the image of a generic sequence.
Due to the increasing complexity of distributed systems the need for a formal description of these systems arises. Specification description languages like SDL enable the formal specification of distributed systems for verification purposes of the system. For simplification of the development process the need for an automatic translation from the specification language to a programming language like Cor C++ arises. High performance and a good readability of the translated code are crucial for the usability of an automatic translation. This paper introduces a framework for the automatic translation of an SDL specification to C++ providing high performance together with good readability of the resulting code. For that we present an object model together with an efficient implementation of the finite state machine with constant costs only using polymorphism. Additionally we present mechanisms to reduce copy and memory allocation operations. A performance evaluation for these mechanisms is also presented. J. Wu et al. (eds.), Formal Methods for Protocol Engineering and Distributed Systems
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