On the exponent of periodicity of minimal solutions of context equations

Context unification is a generalisation of string unification where words are generalized to terms with one hole. Though decidability of string unification was proved by Makanin, the decidability of context unification is currently an open question. This paper provides a step in understanding the complexity of context unification and the structure of unifiers. It is shown, that if a context unification problem of size d is unifiable, then there is also a unifier with an exponent of periodicity smaller than O(21.07d). We also prove NP-hardness for restricted cases of the context unification problem and compare the complexity of general context unification with that of general string unification.