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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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References

Antonik, A. (2008) Decision problems for partial specifications: empirical and worst-case complexity, Ph.D. thesis, Imperial College, London.Google Scholar
Antonik, A. and Huth, M. (2009) On the complexity of semantic self-minimization. In: Proc. AVOCS 2007. Electronic Notes in Theoretical Computer Science 250 3–19.Google Scholar
Antonik, A., Huth, M., Larsen, K. G., Nyman, U. and Wąsowski, A. (2008a) 20 years of modal and mixed specifications. Bulletin of EATCS 95. (Available at http://processalgebra.blogspot.com/2008/05/concurrency-column-for-beatcs-june-2008.html.)Google Scholar
Antonik, A., Huth, M., Larsen, K. G., Nyman, U. and Wąsowski, A. (2008b) Complexity of decision problems for mixed and modal specifications. In: FoSSaCS'08. Springer-Verlag Lecture Notes in Computer Science 4962 112–126.Google Scholar
Antonik, A., Huth, M., Larsen, K. G., Nyman, U. and Wąsowski, A. (2008c) Exptime-complete decision problems for modal and mixed specifications. In: 15th International Workshop on Expressiveness in Concurrency. Electronic Notes in Theoretical Computer Science 242 19–33.CrossRefGoogle Scholar
Beneš, N., Křetínský, J., Larsen, K. G. and Srba, J. (2009) Checking thorough refinement on modal transition systems is EXPTIME-complete. In: Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing. Springer-Verlag Lecture Notes in Computer Science 5684 112–126.Google Scholar
Berwanger, D., Chatterjee, K., Doyen, L., Henzinger, T. A. and Raje, S. (2008) Strategy construction for parity games with imperfect information. In: Proceedings of the 19th International Conference on Concurrency Theory (CONCUR'08). Springer-Verlag Lecture Notes in Computer Science 5201 325–339.CrossRefGoogle Scholar
Berwanger, D. and Doyen, L. (2008) On the power of imperfect information. In: Proceedings of the 28th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS'08), Bangalore, India, December 2008. Available at http://drops.dagstuhl.de/portals/FSTTCS08/.Google Scholar
Børjesson, A., Larsen, K. G. and Skou, A. (1993) Generality in design and compositional verification using tav. In: FORTE '92 Proceedings, North-Holland Publishing Co. 449–464.Google Scholar
Brunet, G., Chechik, M. and Uchitel, S. (2006) Properties of behavioural model merging. In: Misra, J., Nipkow, T. and Sekerinski, E. (eds.) FM. Springer-Verlag Lecture Notes in Computer Science 4085 98–114.CrossRefGoogle Scholar
Bruns, G. (1997) An industrial application of modal process logic. Sci. Comput. Program. 29 (1-2)3–22.CrossRefGoogle Scholar
Bruns, G. and Godefroid, P. (2000) Generalized model checking: Reasoning about partial state spaces. In: Palamidessi, C. (ed.) CONCUR. Springer-Verlag Lecture Notes in Computer Science 1877 168–182.CrossRefGoogle Scholar
Chandra, A. K., Kozen, D. and Stockmeyer, L. J. (1981) Alternation. J. ACM 28 (1)114–133.Google Scholar
Chebyshev, P. (1852) La totalité des nombres premiers inférieurs a une limite donnée. Journal de Mathematiques Pures et Appliques 17 341–365.Google Scholar
Clarke, E. M., Grumberg, O. and Long, D. E. (1994) Model checking and abstraction. ACM Trans. Program. Lang. Syst. 16 (5)1512–1542.CrossRefGoogle Scholar
Dams, D. (1996) Abstract Interpretation and Partition Refinement for Model Checking, Ph.D. thesis, Eindhoven University of Technology.Google Scholar
Fischbein, D., Uchitel, S. and Braberman, V. (2006) A foundation for behavioural conformance in software product line architectures. In: ROSATEA '06 Proceedings, ACM Press 39–48.CrossRefGoogle Scholar
Godefroid, P. and Huth, M. (2005) Model checking vs. generalized model checking: Semantic minimizations for temporal logics. In: Proceedings of the Twentieth Annual IEEE Symp. on Logic in Computer Science, LICS 2005, IEEE Computer Society Press 158–167.Google Scholar
Godefroid, P., Huth, M. and Jagadeesan, R. (2001) Abstraction-based model checking using modal transition systems. In: Larsen, K. G. and Nielsen, M. (eds.) CONCUR 2001 – concurrency theory: 12th international conference, Aalborg, Denmark. Springer-Verlag Lecture Notes in Computer Science 2154 426–440.CrossRefGoogle Scholar
Gurfinkel, A., Wei, O. and Chechik, M. (2006) Yasm: A software model-checker for verification and refutation. In: Ball, T. and Jones, R. B. (eds.) CAV. Springer-Verlag Lecture Notes in Computer Science 4144 170–174.CrossRefGoogle Scholar
Huth, M. (2005a) Labelled transition systems as a Stone space. Logical Methods in Computer Science 1 (1)1–28.Google Scholar
Huth, M. (2005b) Refinement is complete for implementations. Formal Asp. Comput. 17 (2)113–137.Google Scholar
Huth, M., Jagadeesan, R. and Schmidt, D. (2001) Modal transition systems: A foundation for three-valued program analysis. Springer-Verlag Lecture Notes in Computer Science 2028.CrossRefGoogle Scholar
Hüttel, H. (1988) Operational and denotational properties of modal process logic. Master's thesis, Computer Science Department, Aalborg University.Google Scholar
Kozen, D. (1988) A finite model theorem for the propositional μ-calculus. Studia Logica 47 (3)233–241.Google Scholar
Landweber, P. S. (1963) Three theorems on phrase structure grammars of type 1. Information and Control 6 (2)131–136.Google Scholar
Laroussinie, F. and Sproston, J. (2007) State explosion in almost-sure probabilistic reachability. Inf. Process. Lett. 102 (6)236–241.CrossRefGoogle Scholar
Larsen, K. G. (1989) Modal specifications. In Sifakis, J. (ed.) Automatic Verification Methods for Finite State Systems. Springer-Verlag Lecture Notes in Computer Science 407 232–246.Google Scholar
Larsen, K. G., Nyman, U. and Wąsowski, A. (2007a) Modal I/O automata for interface and product line theories. In: Nicola, R. D. (ed.) ESOP. Springer-Verlag Lecture Notes in Computer Science 4421 64–79.CrossRefGoogle Scholar
Larsen, K. G., Nyman, U. and Wąsowski, A. (2007b) On modal refinement and consistency. In: Caires, L. and Vasconcelos, V. T. (eds.) CONCUR 2007. Springer-Verlag Lecture Notes in Computer Science 4703 105–119.Google Scholar
Larsen, K. G., Steffen, B. and Weise, C. (1995) A constraint oriented proof methodology based on modal transition systems. In: Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems. Springer-Verlag Lecture Notes in Computer Science 1019 17–40.CrossRefGoogle Scholar
Larsen, K. G. and Thomsen, B. (1988) A modal process logic. In: Third Annual IEEE Symposium on Logic in Computer Science (LICS), IEEE Computer Society 203–210.Google Scholar
Larsen, K. G. and Xinxin, L. (1990) Equation solving using modal transition systems. In: Fifth Annual IEEE Symposium on Logics in Computer Science (LICS), IEEE Computer Society 108–117.Google Scholar
Nyman, U. (2008) Modal Transition Systems as the Basis for Interface Theories and Product Lines, Ph.D. thesis, Department of Computer Science, Aalborg University.Google Scholar
Park, D. (1981) Concurrency and automata on infinite sequences. In: Proceedings of the 5th GI-Conference on Theoretical Computer Science. Springer-Verlag Lecture Notes in Computer Science 104 167–183.Google Scholar
Raclet, J.-B. (2008) Residual for component specifications. Electronic Notes in Theoretical Computer Science 215 93–110.Google Scholar
Schmidt, D. (2001) From trace sets to modal-transition systems by stepwise abstract interpretation.Google Scholar
Schmidt, H. and Fecher, H. (2007) Comparing disjunctive modal transition systems with a one-selecting variant. (Submitted for publication.)Google Scholar
Sipser, M. (1996) Introduction to the Theory of Computation, PWS Publishing Company.Google Scholar
Uchitel, S. and Chechik, M. (2004) Merging partial behavioural models. In: Taylor, R. N. and Dwyer, M. B. (eds.). SIGSOFT Software Engineering Notes 29 (6) 43–52.Google Scholar
Wilke, Th. (2001) Alternating tree automata, parity games, and modal μ-calculus. Bull. Soc. Math. Belg. 8 (2).Google Scholar
Xinxin, L. (1992) Specification and Decomposition in Concurrency, Ph.D. thesis, Department of Mathematics and Comnputer Science, Aalborg University.Google Scholar
Zielonka, W. (1998) Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci. 200 (1-2)135–183.Google Scholar