11 research outputs found
A 222pn upper bound on the complexity of Presburger Arithmetic
AbstractThe decision problem for the theory of integers under addition, or âPresburger Arithmetic,â is proved to be elementary recursive in the sense of Kalmar. More precisely, it is proved that a quantifier elimination decision procedure for this theory due to Cooper determines, for any n, the truth of any sentence of length n within deterministic time 222pn for some constant p > 1. This upper bound is approximately one exponential higher than the best known lower bound on nondeterministic time. Since it seems to cost one exponential to simulate a nondeterministic algorithm with a deterministic one, it may not be possible to significantly improve either bound
A Modular Toolkit for Distributed Interactions
We discuss the design, architecture, and implementation of a toolkit which
supports some theories for distributed interactions. The main design principles
of our architecture are flexibility and modularity. Our main goal is to provide
an easily extensible workbench to encompass current algorithms and incorporate
future developments of the theories. With the help of some examples, we
illustrate the main features of our toolkit.Comment: In Proceedings PLACES 2010, arXiv:1110.385