Linear Second-Order Unification and Context Unification with Tree-Regular Constraints

Linear Second-Order Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear second-order unification. Here we prove that linear second-order unification can be reduced to context unification with tree-regular constraints. Decidability of context unification is still an open question. We comment on the possibility that linear second-order unification is decidable, if context unification is, and how to get rid of the tree-regular constraints. This is done by reducing rank-bound tree-regular constraints to word-regular constraints.

• Type: Conference
• Year: 2000
• Where: RTA
• Authors: Jordi Levy, Mateu Villaret
• Keywords: Context Unification, Linear Second-order Unification, RTA 2000, Theoretical Computer Science, Tree-regular Constraints