Geodesic
A Type System Describing Unboundedness
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 4.

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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.
DOI : 10.23638/DMTCS-22-4-2
Classification : 03B40, 03D05, 68Q17, 68Q45 
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Parys, Paweł. A Type System Describing Unboundedness. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 4. doi : 10.23638/DMTCS-22-4-2. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-4-2/

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