Universal Witnesses for State Complexity of Boolean Operations and Concatenation Combined with Star

We study the state complexity of boolean operations and product (concatenation, catenation) combined with star. We derive tight upper bounds for the symmetric differences and differences of two languages, one or both of which are starred, and for the product of two starred languages. We prove that the previously discovered bounds for the union and the intersection of languages with one or two starred arguments, for the product of two languages one of which is starred, and for the star of the product of two languages, can all be met by the recently introduced universal witnesses and their variants.

[1]  Yuan Gao,et al.  State Complexity of Combined Operations with Two Basic Operations , 2022 .

[2]  Arto Salomaa,et al.  State complexity of combined operations , 2007, Theor. Comput. Sci..

[3]  Janusz A. Brzozowski,et al.  In Search of Most Complex Regular Languages , 2012, Int. J. Found. Comput. Sci..

[4]  Pascal Caron,et al.  From Glushkov WFAs to K-Expressions , 2011, Fundam. Informaticae.

[5]  Yuan Gao,et al.  State Complexity of Two Combined Operations: Catenation-Star and Catenation-Reversal , 2012, Int. J. Found. Comput. Sci..

[6]  Sheng Yu,et al.  State Complexity of Regular Languages , 2001, J. Autom. Lang. Comb..

[7]  Yuan Gao,et al.  State Complexity of Combined Operations with Union, Intersection, Star and Reversal , 2012, Fundam. Informaticae.

[8]  Alexander Okhotin,et al.  On the State Complexity of Star of Union and Star of Intersection , 2011, Fundam. Informaticae.

[9]  Igor Potapov,et al.  On the Computational Complexity of Matrix Semigroup Problems , 2012, Fundam. Informaticae.

[10]  Janusz A. Brzozowski.  Quotient Complexity of Regular Languages , 2010, J. Autom. Lang. Comb..

[11]  Yuan Gao,et al.  The State Complexity of Two Combined Operations: Star of Catenation and Star of Reversal , 2008, Fundam. Informaticae.

[12]  Yuan Gao,et al.  State complexity of union and intersection of star on k regular languages , 2012, Theor. Comput. Sci..

[13]  Carlos Martín-Vide,et al.  State Complexity of Basic Operations Combined with Reversal , 2007, LATA.