TL;DR
This paper investigates the limitations of visibly pushdown languages, showing that their hierarchical structure remains invisible to finite automata and that certain decision problems like separability are undecidable.
Contribution
It demonstrates that the structure in visibly pushdown languages remains invisible to finite automata and proves undecidability of separability with regular languages.
Findings
Structure remains invisible to finite automata
Separability with regular languages is undecidable
Visibly pushdown languages share undecidability properties with context-free languages
Abstract
Context free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these properties by making the structure of the tree visible, such as is done by visibly pushdown languages, or finite automata on trees. In this paper, we show that the structure given by such approaches remains invisible when it is read by a finite automaton (on word). In particular, we show that separability with a regular language is undecidable for visibly pushdown languages, just as it is undecidable for general context free languages.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Machine Learning and Algorithms