Boolean Language Equations

  • Ernst L. Leiss
Part of the Monographs in Computer Science book series (MCS)

Abstract

We define boolean language equations and relate them to boolean automata. Boolean language equations are explicit equations over an arbitrary alphabet in which union, left-concatenation, and complementation may occur. Boolean automata are a generalization of nondeterministic finite automata that are able to accommodate, in a natural way, the complementation operation. We first show that not every boolean equation has a solution. Then, we give a constructive approach to solving any system of boolean equations that has a solution. We also give a complete characterization of the existence of solutions, decide whether more than one solution exists, give a representation of all solutions if more than one exists, and show that any boolean equation whose constant languages are regular must have a regular solution, if it has any.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Ernst L. Leiss
    • 1
  1. 1.Department of Computer ScienceUniversity of HoustonHoustonUSA

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