Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Formal languages over GF(2). / Bakinova, Ekaterina; Basharin, Artem; Batmanov, Igor; Lyubort, Konstantin; Okhotin, Alexander; Sazhneva, Elizaveta.
в: Information and Computation, Том 283, 104672, 01.02.2022.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Formal languages over GF(2)
AU - Bakinova, Ekaterina
AU - Basharin, Artem
AU - Batmanov, Igor
AU - Lyubort, Konstantin
AU - Okhotin, Alexander
AU - Sazhneva, Elizaveta
N1 - Publisher Copyright: © 2020 Elsevier Inc.
PY - 2022/2/1
Y1 - 2022/2/1
N2 - Variants of the union and concatenation operations on formal languages are investigated, in which Boolean logic in the definitions (that is, conjunction and disjunction) is replaced with the operations in the two-element field GF(2) (conjunction and exclusive OR). Union is thus replaced with symmetric difference, whereas concatenation gives rise to a new GF(2)-concatenation operation, which is notable for being invertible. All operations preserve regularity, and for a pair of languages recognized by an m-state and an n-state DFA, their GF(2)-concatenation is recognized by a DFA with m⋅2n states, and this number of states is in the worst case necessary. Similarly, the state complexity of GF(2)-inverse is 2n+1. Next, a new class of formal grammars based on GF(2)-operations is defined, and it is shown to have the same computational complexity as ordinary grammars with union and concatenation: in particular, simple parsing in time O(n3), fast parsing in the time of matrix multiplication, and parsing in NC2.
AB - Variants of the union and concatenation operations on formal languages are investigated, in which Boolean logic in the definitions (that is, conjunction and disjunction) is replaced with the operations in the two-element field GF(2) (conjunction and exclusive OR). Union is thus replaced with symmetric difference, whereas concatenation gives rise to a new GF(2)-concatenation operation, which is notable for being invertible. All operations preserve regularity, and for a pair of languages recognized by an m-state and an n-state DFA, their GF(2)-concatenation is recognized by a DFA with m⋅2n states, and this number of states is in the worst case necessary. Similarly, the state complexity of GF(2)-inverse is 2n+1. Next, a new class of formal grammars based on GF(2)-operations is defined, and it is shown to have the same computational complexity as ordinary grammars with union and concatenation: in particular, simple parsing in time O(n3), fast parsing in the time of matrix multiplication, and parsing in NC2.
KW - Computational complexity
KW - Finite automata
KW - Finite fields
KW - Formal grammars
KW - Formal languages
KW - Parsing
KW - State complexity
KW - RECOGNITION
KW - CONJUNCTIVE GRAMMARS
KW - OPERATIONS
KW - COMPLEXITY
KW - EQUATIONS
UR - http://www.scopus.com/inward/record.url?scp=85098193882&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/a1e1719a-5a19-3dee-a8b6-7f0f644ca025/
U2 - 10.1016/j.ic.2020.104672
DO - 10.1016/j.ic.2020.104672
M3 - Article
AN - SCOPUS:85098193882
VL - 283
JO - Information and Computation
JF - Information and Computation
SN - 0890-5401
M1 - 104672
ER -
ID: 92751015