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Equations Over ω-Automata

  • Tiziano Villa
  • Nina Yevtushenko
  • Robert K. Brayton
  • Alan Mishchenko
  • Alexandre Petrenko
  • Alberto Sangiovanni-Vincentelli
Chapter

Abstract

An infinite word over an alphabet A, or ω-word, is an infinite sequence of symbols of A. Aω is the set of ω-words on A. An ω-language on A is a subset of Aω. Moreover, A = AAω. An ω-word may be written as \(\alpha = \alpha (0)\alpha (1)\ldots \), where α(i) ∈ A for every i ≥ 0; if nm, \(\alpha (n,m) = \alpha (n)\ldots \alpha (m - 1)\alpha (m)\) and \(\alpha (n,\infty ) = \alpha (n)\alpha (n + 1)\ldots \). The notations ∃ωn stands for ’there are infinitely many n’ and ∃< ωn stands for ’there are finitely many n’.

Keywords

Infinite Sequence Finite Automaton Acceptance Condition Parallel Equation Persistent State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Tiziano Villa
    • 1
  • Nina Yevtushenko
    • 2
  • Robert K. Brayton
    • 3
  • Alan Mishchenko
    • 4
  • Alexandre Petrenko
    • 5
  • Alberto Sangiovanni-Vincentelli
    • 4
  1. 1.Dipartimento D’InformaticaUniversità di VeronaVeronaItaly
  2. 2.Department of EECSTomsk State UniversityTomskRussia
  3. 3.Department of Electrical Engineering and Computer ScienceUniversity of CaliforniaBerkeleyUSA
  4. 4.Department of Electrical Engineering and Computer Science (EECS)University of California, BerkeleyBerkeleyUSA
  5. 5.Computer Research Institute of Montreal (CRIM)MontrealCanada

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