License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.63
URN: urn:nbn:de:0030-drops-145037
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14503/
Jančar, Petr ;
Šíma, Jiří
The Simplest Non-Regular Deterministic Context-Free Language
Abstract
We introduce a new notion of ?-simple problems for a class ? of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is ?-simple if it can be reduced to each problem in ?. This can be viewed as a conceptual counterpart to ?-hard problems to which all problems in ? reduce. Our concrete example is the class of non-regular deterministic context-free languages (DCFL'), with a truth-table reduction by Mealy machines. The main technical result is a proof that the DCFL' language L_# = {0^n1^n ∣ n ≥ 1} is DCFL'-simple, and can be thus viewed as one of the simplest languages in the class DCFL', in a precise sense. The notion of DCFL'-simple languages is nontrivial: e.g., the language L_R = {wcw^R∣ w ∈ {a,b}^*} is not DCFL'-simple.
By describing an application in the area of neural networks (elaborated in another paper), we demonstrate that ?-simple problems under suitable reductions can provide a tool for expanding the lower-bound results known for single problems to the whole classes of problems.
BibTeX - Entry
@InProceedings{jancar_et_al:LIPIcs.MFCS.2021.63,
author = {Jan\v{c}ar, Petr and \v{S}{\'\i}ma, Ji\v{r}{\'\i}},
title = {{The Simplest Non-Regular Deterministic Context-Free Language}},
booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
pages = {63:1--63:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-201-3},
ISSN = {1868-8969},
year = {2021},
volume = {202},
editor = {Bonchi, Filippo and Puglisi, Simon J.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14503},
URN = {urn:nbn:de:0030-drops-145037},
doi = {10.4230/LIPIcs.MFCS.2021.63},
annote = {Keywords: deterministic context-free language, truth-table reduction, Mealy automaton, pushdown automaton}
}
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Keywords: |
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deterministic context-free language, truth-table reduction, Mealy automaton, pushdown automaton |
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Collection: |
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46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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18.08.2021 |
