Simplifying the Signature in Second-Order Unification

Second-Order Unification is undecidable even for very specialized fragments. The signature plays a crucial role in these fragments. If all symbols are monadic, then the problem is NP-complete, whereas it is enough to have just one binary constant to lose decidability. In this work we reduce Second-Order Unification to Second-Order Unification with a signature that contains just one binary function symbol and constants. The reduction is based on partially currying the equations by using the binary function symbol for explicit application @. Our work simplifies the study of Second-Order Unification and some of its variants, like Context Unification and Bounded Second-Order Unification. Source URL: https://www.iiia.csic.es/en/node/54044 Links [1] https://www.iiia.csic.es/en/staff/jordi-levy [2] https://www.iiia.csic.es/en/staff/mateu-villaret [3] https://www.iiia.csic.es/en/bibliography?f[keyword]=812 [4] https://www.iiia.csic.es/en/bibliography?f[keyword]=835 [5] https://www.iiia.csic.es/en/bibliography?f[keyword]=814