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Decidable Compositions of O-Minimal Automata

  • Alberto Casagrande
  • Pietro Corvaja
  • Carla Piazza
  • Bud Mishra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5311)

Abstract

We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this paper is able to show that when one focuses on the composition of semi-algebraic o-minimal automata, it is possible to translate the decidability problem into a satisfiability problem over formulæinvolving both real and integer variables. While in the general case such formulæ would be undecidable, the particular format of the formulæ obtained in our translation allows combining decidability results stemming from both algebraic number theory and first-order logic over (ℝ, 0, 1, + , *, < ) to yield a novel decidability algorithm. From a more general perspective, this paper exposes many new open questions about decidable combinations of real/integer logics.

Keywords

Algebraic Number Parallel Composition Reachability Condition Discrete Transition Simple Cycle 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alberto Casagrande
    • 1
    • 2
    • 3
  • Pietro Corvaja
    • 2
  • Carla Piazza
    • 2
  • Bud Mishra
    • 4
    • 5
  1. 1.Istituto di Genomica ApplicataUdineItaly
  2. 2.DIMI, Università di UdineUdineItaly
  3. 3.DISA, Università di UdineUdineItaly
  4. 4.Courant Institute of Mathematical ScienceNYUNew YorkU.S.A.
  5. 5.NYU School of MedicineNew YorkU.S.A.

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