On the Complexity of Consistency and Complete State Coding for Signal Transition Graphs

  • Authors:
  • Javier Esparza;Petr Jančar;Alexander Miller

  • Affiliations:
  • (Correspd.) Institut für Informatik, Technische Universität München, Germany. esparza@in.tum.de;Center of Applied Cybernetics, Dept of CS, TU Ostrava, Czechia. Petr.Jancar@vsb.cz;Institute for Formal Methods in Computer Science, Univ. Stuttgart, Germany. Alexander.Miller@informatik.uni-stuttgart.de

  • Venue:
  • Fundamenta Informaticae - Application of Concurrency to System Design (ACSD'06)
  • Year:
  • 2008

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Abstract

Signal Transition Graphs (STGs) are a popular formalism for the specification of asynchronous circuits. A necessary condition for the implementability of an STG is the existence of a consistent and complete state encoding. For an important subclass of STGs, the marked graph STGs, we show that checking consistency is polynomial, but checking the existence of a complete state coding is co-NP-complete. In fact, co-NP-completeness already holds for acyclic and 1-bounded marked graph STGs and for live and 1-bounded marked graph STGs. We add some relevant results for free-choice, bounded, and general STGs.