Context Uni cation and Traversal Equations

Context uniication was originally deened by H. Comon in ICALP'92, as the problem of nding a uniier for a set of equations containing rst-order variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are second-order variables that are restricted to be instantiated by linear terms (a linear term is a-expression x1 xn : t where every xi occur exactly once in t). In this paper, we prove that, if the so called rank-bounded conjecture is true, then the context uniication problem is decidable. This is done reducing context uniication to solvability of traversal equations (a kind of word uniication modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints.