A Type System Describing Unboundedness

Paweł Parys (1)

1 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

We consider nondeterministic higher-order recursion schemes as recognizers of languages of finite words or finite trees. We propose a type system that allows to solve the simultaneous-unboundedness problem (SUP) for schemes, which asks, given a set of letters A and a scheme G, whether it is the case that for every number n the scheme accepts a word (a tree) in which every letter from A appears at least n times. Using this type system we prove that SUP is (m-1)-EXPTIME-complete for word-recognizing schemes of order m, and m-EXPTIME-complete for tree-recognizing schemes of order m. Moreover, we establish the reflection property for SUP: out of an input scheme G one can create its enhanced version that recognizes the same language but is aware of the answer to SUP.

Mots clés: simultaneous-unboundedness problem; higher-order recursion schemes; intersection types; reflection

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]; Complexité [cs.CC]

Paweł Parys. A Type System Describing Unboundedness. Discrete Mathematics and Theoretical Computer Science, 2020, vol. 22 no. 4, ⟨10.23638/DMTCS-22-4-2⟩. ⟨hal-01850934v4⟩