The paper investigates the expressive power of language equations with the operations of concatenation and symmetric difference. For equations over every finite alphabet Σ with Σ ≥ 1, it is demonstrated that the sets representable by unique solutions of such equations are exactly the recursive sets over Σ, and the sets representable by their least (greatest) solutions are exactly the recursively enumerable sets (their complements, respectively). If - ≥ 2, the same characterization holds already for equations using symmetric difference and linear concatenation with regular constants. In both cases, the solution existence problem is 0 1-complete, the existence of a unique, a least or a greatest solution is 0 2-complete, while the existence of finitely many solutions is 0 3-complete.

Original languageEnglish
Pages (from-to)205-222
Number of pages18
JournalFundamenta Informaticae
Issue number1-4
Publication statusPublished - 28 May 2012

Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Information Systems
  • Computational Theory and Mathematics

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