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A Type System Describing Unboundedness
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Journal Article
A Type System Describing Unboundedness
2020
Overview
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.
Publisher
DMTCS,Discrete Mathematics & Theoretical Computer Science
Subject
[info.info-cc]computer science [cs]/computational complexity [cs.cc]
/ [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]
/ Formal Languages and Automata Theory
/ higher-order recursion schemes
