Standard

On language equations with concatenation and various sets of boolean operations. / Okhotin, Alexander.

In: RAIRO - Theoretical Informatics and Applications, Vol. 49, No. 3, 01.07.2015, p. 205-232.

Research output: Contribution to journal › Article › peer-review

Harvard

Okhotin, A 2015, 'On language equations with concatenation and various sets of boolean operations', RAIRO - Theoretical Informatics and Applications, vol. 49, no. 3, pp. 205-232. https://doi.org/10.1051/ita/2015006

APA

Okhotin, A. (2015). On language equations with concatenation and various sets of boolean operations. RAIRO - Theoretical Informatics and Applications, 49(3), 205-232. https://doi.org/10.1051/ita/2015006

Vancouver

Okhotin A. On language equations with concatenation and various sets of boolean operations. RAIRO - Theoretical Informatics and Applications. 2015 Jul 1;49(3):205-232. https://doi.org/10.1051/ita/2015006

Author

Okhotin, Alexander. / On language equations with concatenation and various sets of boolean operations. In: RAIRO - Theoretical Informatics and Applications. 2015 ; Vol. 49, No. 3. pp. 205-232.

BibTeX

@article{6fdb0acaf25d4606b2600e410cbcaada,
title = "On language equations with concatenation and various sets of boolean operations",
abstract = "Systems of equations of the form Xi = ℓi(X1, . . .,Xn), for 1 ≤i ≤ n, in which the unknowns Xi are formal languages, and the right-hand sides ≤i may contain concatenation and union, are known for representing context-free grammars. If, instead of union only, another set of Boolean operations is used, the expressive power of such equations may change: for example, using both union and intersection leads to conjunctive grammars [A. Okhotin, J. Automata, Languages and Combinatorics 6 (2001) 519-535], whereas using all Boolean operations allows all recursive sets to be expressed by unique solutions [A. Okhotin, Decision problems for language equations with Boolean operations, Automata, Languages and Programming, ICALP 2003, Eindhoven, The Netherlands, 239-251]. This paper investigates the expressive power of such equations with any possible set of Boolean operations. It is determined that different sets of Boolean operations give rise to exactly seven families of formal languages: the recursive languages, the conjunctive languages, the context-free languages, a certain family incomparable with the context-free languages, as well as three subregular families.",
author = "Alexander Okhotin",
year = "2015",
month = jul,
day = "1",
doi = "10.1051/ita/2015006",
language = "English",
volume = "49",
pages = "205--232",
journal = "RAIRO - Theoretical Informatics and Applications",
issn = "0988-3754",
publisher = "EDP Sciences",
number = "3",

}

RIS

TY - JOUR

T1 - On language equations with concatenation and various sets of boolean operations

AU - Okhotin, Alexander

PY - 2015/7/1

Y1 - 2015/7/1

N2 - Systems of equations of the form Xi = ℓi(X1, . . .,Xn), for 1 ≤i ≤ n, in which the unknowns Xi are formal languages, and the right-hand sides ≤i may contain concatenation and union, are known for representing context-free grammars. If, instead of union only, another set of Boolean operations is used, the expressive power of such equations may change: for example, using both union and intersection leads to conjunctive grammars [A. Okhotin, J. Automata, Languages and Combinatorics 6 (2001) 519-535], whereas using all Boolean operations allows all recursive sets to be expressed by unique solutions [A. Okhotin, Decision problems for language equations with Boolean operations, Automata, Languages and Programming, ICALP 2003, Eindhoven, The Netherlands, 239-251]. This paper investigates the expressive power of such equations with any possible set of Boolean operations. It is determined that different sets of Boolean operations give rise to exactly seven families of formal languages: the recursive languages, the conjunctive languages, the context-free languages, a certain family incomparable with the context-free languages, as well as three subregular families.

AB - Systems of equations of the form Xi = ℓi(X1, . . .,Xn), for 1 ≤i ≤ n, in which the unknowns Xi are formal languages, and the right-hand sides ≤i may contain concatenation and union, are known for representing context-free grammars. If, instead of union only, another set of Boolean operations is used, the expressive power of such equations may change: for example, using both union and intersection leads to conjunctive grammars [A. Okhotin, J. Automata, Languages and Combinatorics 6 (2001) 519-535], whereas using all Boolean operations allows all recursive sets to be expressed by unique solutions [A. Okhotin, Decision problems for language equations with Boolean operations, Automata, Languages and Programming, ICALP 2003, Eindhoven, The Netherlands, 239-251]. This paper investigates the expressive power of such equations with any possible set of Boolean operations. It is determined that different sets of Boolean operations give rise to exactly seven families of formal languages: the recursive languages, the conjunctive languages, the context-free languages, a certain family incomparable with the context-free languages, as well as three subregular families.

UR - http://www.scopus.com/inward/record.url?scp=85006833233&partnerID=8YFLogxK

U2 - 10.1051/ita/2015006

DO - 10.1051/ita/2015006

M3 - Article

AN - SCOPUS:85006833233

VL - 49

SP - 205

EP - 232

JO - RAIRO - Theoretical Informatics and Applications

JF - RAIRO - Theoretical Informatics and Applications

SN - 0988-3754

IS - 3

ER -

ID: 41137800