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Modal and mixed specifications: key decision problems and their complexities

Published online by Cambridge University Press:  26 February 2010

ADAM ANTONIK ,
MICHAEL HUTH ,
KIM G. LARSEN ,
ULRIK NYMAN  and
ANDRZEJ WĄSOWSKI
ADAM ANTONIK
Affiliation:
CNRS, Ecole Normale Supérieure de Cachan, France Email: antonik@lsv.ens-cachan.fr
MICHAEL HUTH
Affiliation:
Department of Computing, Imperial College London, United Kingdom Email: m.huth@imperial.ac.uk
KIM G. LARSEN
Affiliation:
Department of Computer Science, Aalborg University, Denmark Email: kgl@cs.aau.dk; ulrik@cs.aau.dk
ULRIK NYMAN
Affiliation:
Department of Computer Science, Aalborg University, Denmark Email: kgl@cs.aau.dk; ulrik@cs.aau.dk
ANDRZEJ WĄSOWSKI
Affiliation:
IT University of Copenhagen, Denmark Email: wasowski@itu.dk
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Abstract

Modal and mixed transition systems are specification formalisms that allow the mixing of over- and under-approximation. We discuss three fundamental decision problems for such specifications:

  • — whether a set of specifications has a common implementation;

  • — whether an individual specification has an implementation; and

  • — whether all implementations of an individual specification are implementations of another one.

For each of these decision problems we investigate the worst-case computational complexity for the modal and mixed cases. We show that the first decision problem is EXPTIME-complete for both modal and mixed specifications. We prove that the second decision problem is EXPTIME-complete for mixed specifications (it is known to be trivial for modal ones). The third decision problem is also shown to be EXPTIME-complete for mixed specifications.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 1: Expressiveness in Concurrency 2008 , February 2010 , pp. 75 - 103
Copyright
Copyright © Cambridge University Press 2010

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