Formal Languages over GF(2)

  • Ekaterina Bakinova
  • Artem Basharin
  • Igor Batmanov
  • Konstantin Lyubort
  • Alexander Okhotin
  • Elizaveta Sazhneva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)


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 their state complexity is determined. 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.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Gymnasium №1KovrovRussia
  2. 2.School №179MoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  4. 4.St. Petersburg Academic UniversitySaint PetersburgRussia
  5. 5.St. Petersburg State UniversitySaint PetersburgRussia

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