### Abstract

GF(2)-grammars, recently introduced by Bakinova et al. (“ Formal languages over GF(2) ”, LATA 2018), are a variant of ordinary context-free grammars, in which the disjunction is replaced by exclusive OR, whereas the classical concatenation is replaced by a new operation called GF(2)-concatenation: KʘL is the set of all strings with an odd number of partitions into a concatenation of a string in K and a string in L. This paper establishes several results on the family of languages defined by these grammars. Over the unary alphabet, GF(2)-grammars define exactly the 2-automatic sets. No language of the form (formula Presented), with uniformly superlinear f, can be described by any GF(2)-grammar. The family is not closed under union, intersection, classical concatenation and Kleene star, non-erasing homomorphisms. On the other hand, this family is closed under injective nondeterministic finite transductions, and contains a hardest language under reductions by homomorphisms.

Original language | English |
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Title of host publication | SOFSEM 2019 |

Subtitle of host publication | Theory and Practice of Computer Science - 45th International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings |

Editors | Rastislav Královič, Giovanni Pighizzini, Jerzy Nawrocki, Barbara Catania |

Publisher | Springer |

Pages | 310-323 |

Number of pages | 14 |

ISBN (Print) | 9783030108007 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | 45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018 - Nový Smokovec Duration: 27 Jan 2019 → 30 Jan 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11376 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018 |
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Country | Slovakia |

City | Nový Smokovec |

Period | 27/01/19 → 30/01/19 |

### Fingerprint

### Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*SOFSEM 2019: Theory and Practice of Computer Science - 45th International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings*(pp. 310-323). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11376 LNCS). Springer. https://doi.org/10.1007/978-3-030-10801-4_25

}

*SOFSEM 2019: Theory and Practice of Computer Science - 45th International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11376 LNCS, Springer, pp. 310-323, Nový Smokovec, 27/01/19. https://doi.org/10.1007/978-3-030-10801-4_25

**On the expressive power of GF(2)-grammars.** / Makarov, Vladislav; Okhotin, Alexander.

Research output

TY - GEN

T1 - On the expressive power of GF(2)-grammars

AU - Makarov, Vladislav

AU - Okhotin, Alexander

PY - 2019/1/1

Y1 - 2019/1/1

N2 - GF(2)-grammars, recently introduced by Bakinova et al. (“ Formal languages over GF(2) ”, LATA 2018), are a variant of ordinary context-free grammars, in which the disjunction is replaced by exclusive OR, whereas the classical concatenation is replaced by a new operation called GF(2)-concatenation: KʘL is the set of all strings with an odd number of partitions into a concatenation of a string in K and a string in L. This paper establishes several results on the family of languages defined by these grammars. Over the unary alphabet, GF(2)-grammars define exactly the 2-automatic sets. No language of the form (formula Presented), with uniformly superlinear f, can be described by any GF(2)-grammar. The family is not closed under union, intersection, classical concatenation and Kleene star, non-erasing homomorphisms. On the other hand, this family is closed under injective nondeterministic finite transductions, and contains a hardest language under reductions by homomorphisms.

AB - GF(2)-grammars, recently introduced by Bakinova et al. (“ Formal languages over GF(2) ”, LATA 2018), are a variant of ordinary context-free grammars, in which the disjunction is replaced by exclusive OR, whereas the classical concatenation is replaced by a new operation called GF(2)-concatenation: KʘL is the set of all strings with an odd number of partitions into a concatenation of a string in K and a string in L. This paper establishes several results on the family of languages defined by these grammars. Over the unary alphabet, GF(2)-grammars define exactly the 2-automatic sets. No language of the form (formula Presented), with uniformly superlinear f, can be described by any GF(2)-grammar. The family is not closed under union, intersection, classical concatenation and Kleene star, non-erasing homomorphisms. On the other hand, this family is closed under injective nondeterministic finite transductions, and contains a hardest language under reductions by homomorphisms.

UR - http://www.scopus.com/inward/record.url?scp=85062357069&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/expressive-power-gf2grammars

U2 - 10.1007/978-3-030-10801-4_25

DO - 10.1007/978-3-030-10801-4_25

M3 - Conference contribution

AN - SCOPUS:85062357069

SN - 9783030108007

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 310

EP - 323

BT - SOFSEM 2019

A2 - Královič, Rastislav

A2 - Pighizzini, Giovanni

A2 - Nawrocki, Jerzy

A2 - Catania, Barbara

PB - Springer

ER -