Logic in Computer Science (LICS 1997)

Paper: On the Complexity of Reasoning in Kleene Algebra (at LICS 1997)

Authors: Dexter Kozen

Abstract

We study the complexity of reasoning in Kleene algebra and *-continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E --> s=t, where E is a finite set of equations. We obtain various levels of complexity based on the form of the assumptions E. Our main results are: for *-continuous Kleene algebra, (i) if E contains only commutativity assumptions pq=qp, the problem is Pi-0-1-complete; (ii) if E contains only monoid equations, the problem is Pi-0-2-complete; (iii) for arbitrary equations E, the problem is Pi-1-1-complete. The last problem is the universal Horn theory of the *-continuous Kleene algebras. This resolves an open question of Kozen (1994).

BibTeX

  @InProceedings{Kozen-OntheComplexityofRe,
    author = 	 {Dexter Kozen},
    title = 	 {On the Complexity of Reasoning in Kleene Algebra},
    booktitle =  {Proceedings of the Twelfth Annual IEEE Symp. on Logic in Computer Science, {LICS} 1997},
    year =	 1997,
    editor =	 {Glynn Winskel},
    month =	 {June}, 
    pages =      {195--202},
    location =   {Warsaw, Poland}, 
    publisher =	 {IEEE Computer Society Press}
  }