Distilling common randomness from bipartite quantum states
Igor Devetak, Andreas Winter
ISIT 2003
Many natural specifications use types. We investigate the decidability of fragments of many-sorted first-order logic. We identified some decidable fragments and illustrated their usefulness by formalizing specifications considered in the literature. Often the intended interpretations of specifications are finite. We prove that the formulas in these fragments are valid iff they are valid over the finite structures. We extend these results to logics that allow a restricted form of transitive closure. We tried to extend the classical classification of the quantifier prefixes into decidable/undecidable classes to the many-sorted logic. However, our results indicate that a naive extension fails and more subtle classification is needed. © 2009 Elsevier Ltd. All rights reserved.
Igor Devetak, Andreas Winter
ISIT 2003
R.A. Brualdi, A.J. Hoffman
Linear Algebra and Its Applications
Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
Matthew A Grayson
Journal of Complexity