On the complexity of bounded second-order unification and stratified context unification

Bounded Second-Order Unification is a decidable variant of undecidable Second-Order Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a long-standing open problem. This paper is a join of two separate previous, preliminary papers on NP-completeness of Bounded Second-Order Unification and Stratified Context Unification. It clarifies some omissions in these papers, joins the algorithmic parts that construct a minimal solution, and gives a clear account of a method of using singleton tree grammars for compression that may have potential usage for other algorithmic questions in related areas. © The Author 2010. Published by Oxford University Press. All rights reserved.This research has been partially supported by the research projects Mulog-2 (TIN2007-68005-C04-01) and SuRoS TIN2008-04547) funded by the CICyTPeer Reviewe