Complexity Analysis: Transformation Monoids of Finite Automata

  • Christian BrandlEmail author
  • Hans Ulrich Simon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


We examine the computational complexity of some problems from algebraic automata theory and from the field of communication complexity: testing Green’s relations (relations that are fundamental in monoid theory), checking the property of a finite monoid to have only Abelian subgroups, and determining the deterministic communication complexity of a regular language. By well-known algebraizations, these problems are closely linked with each other. We show that all of them are PSPACE-complete.


Green’s relations Finite monoids Regular languages Communication complexity PSPACE-completeness 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Theoretical Computer Science, Faculty of MathematicsRuhr-University BochumBochumGermany

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