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.

Source : oai:HAL:hal-01850934v4

Volume: vol. 22 no. 4

Section: Automata, Logic and Semantics

Published on: August 18, 2020

Submitted on: August 13, 2018

Keywords: simultaneous-unboundedness problem,higher-order recursion schemes,intersection types,reflection,[INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL],[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO],[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]

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