A Type System Describing Unboundedness

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...

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Vydáno v:Discrete Mathematics and Theoretical Computer Science Ročník 22 no. 4; číslo Automata, Logic and Semantics; s. 1 - 84
Hlavní autor: Parys, Paweł
Médium: Journal Article
Jazyk:angličtina
Vydáno: Nancy DMTCS 01.08.2020
Discrete Mathematics & Theoretical Computer Science
Témata:
[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]
Computational Complexity
Computer Science
Finite sets
Formal Languages and Automata Theory
higher-order recursion schemes
intersection types
Logic in Computer Science
Mathematical research
Recursive functions
reflection
simultaneous-unboundedness problem
Trees (Graph theory)
Words (language)
Poland
intersection types
simultaneous-unboundedness problem
higher-order recursion schemes
reflection
ISSN:1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.23638/DMTCS-22-4-2