State Complexity of GF(2)-Concatenation and GF(2)-Inverse on Unary Languages

  • Alexander OkhotinEmail author
  • Elizaveta Sazhneva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11612)


The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages recognized by an m-state and an n-state DFA is recognized by a DFA with 2mn states, and this number of states is necessary in the worst case, as long as m and n are relatively prime. This operation is known to have an inverse, and the state complexity of the GF(2)-inverse operation over a unary alphabet is proved to be exactly \(2^{n-1}+1\).


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© IFIP International Federation for Information Processing 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySaint PetersburgRussia

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