The Simplest Non-Regular Deterministic Context-Free Language

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73607811" target="_blank" >RIV/61989592:15310/21:73607811 - isvavai.cz</a>

Výsledek na webu

<a href="https://drops.dagstuhl.de/opus/portals/lipics/index.php?semnr=16204" target="_blank" >https://drops.dagstuhl.de/opus/portals/lipics/index.php?semnr=16204</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.63" target="_blank" >10.4230/LIPIcs.MFCS.2021.63</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Simplest Non-Regular Deterministic Context-Free Language

Popis výsledku v původním jazyce

We introduce a new notion of C-simple problems for a class C of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is C-simple if it can be reduced to each problem in C. This can be viewed as a conceptual counterpart to C-hard problems to which all problems in C 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# = {0n1n | 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 LR = {wcwR | w ∈ {a, b}} is not DCFL′-simple. By describing an application in the area of neural networks (elaborated in another paper), we demonstrate that C-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.

Název v anglickém jazyce

The Simplest Non-Regular Deterministic Context-Free Language

Popis výsledku anglicky

We introduce a new notion of C-simple problems for a class C of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is C-simple if it can be reduced to each problem in C. This can be viewed as a conceptual counterpart to C-hard problems to which all problems in C 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# = {0n1n | 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 LR = {wcwR | w ∈ {a, b}} is not DCFL′-simple. By describing an application in the area of neural networks (elaborated in another paper), we demonstrate that C-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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021).

ISBN

978-3-95977-201-3

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

18

Strana od-do

"63-1"-"63-18"

Název nakladatele

LIPICS

Místo vydání

Leibniz

Místo konání akce

Tallinn, Estonia

Datum konání akce

23. 8. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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