The Diagonal Problem for Higher-Order Recursion Schemes is Decidable

Lorenzo Clemente (1) , Paweł Parys (2) , Sylvain Salvati (3) , Igor Walukiewicz (3)

1 UW - University of Warsaw
2 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidabil-ity of the diagonal problem for schemes. This result has several interesting consequences. In particular, it gives an algorithm that computes the downward closure of languages of words recognized by schemes. In turn, this has immediate application to separability problems and reachability analysis of concurrent systems.

Mots clés: downward closure; separability problem; diagonal prob- lem; higher-order recursion schemes; higher-order OI grammars

Domaines: Logique en informatique [cs.LO]

Lorenzo Clemente, Paweł Parys, Sylvain Salvati, Igor Walukiewicz. The Diagonal Problem for Higher-Order Recursion Schemes is Decidable. LICS, Jun 2016, New York, United States. pp.96 - 105, ⟨10.1145/2933575.2934527⟩. ⟨hal-01394830⟩