Abstract
Modal transition systems (MTS) is a well established formalism used for specification and for abstract interpretation. We consider its disjunctive extension (DMTS) and we provide algorithms showing that refinement problems for DMTS are not harder than in the case of MTS. There are two main results in the paper. Firstly, we identify an error in a previous attempt at LTL model checking of MTS and provide algorithms for LTL model checking of MTS and DMTS. Moreover, we show how to apply this result to compositional verification and circumvent the general incompleteness of the MTS composition. Secondly, we give a solution to the common implementation and conjunctive composition problems lowering the complexity from EXPTIME to PTIME.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Larsen, K.G., Nyman, U., Wasowski, A.: Modeling software product lines using color-blind transition systems. STTT 9(5-6), 471–487 (2007)
Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS, pp. 203–210. IEEE Computer Society, Los Alamitos (1988)
Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: 20 years of modal and mixed specifications. Bulletin of the EATCS (95), 94–129 (2008)
Raclet, J.B.: Residual for component specifications. In: Proc. of the 4th International Workshop on Formal Aspects of Component Software (2007)
Bertrand, N., Pinchinat, S., Raclet, J.B.: Refinement and consistency of timed modal specifications. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 152–163. Springer, Heidelberg (2009)
Raclet, J.B., Badouel, E., Benveniste, A., Caillaud, B., Passerone, R.: Why are modalities good for interface theories? In: ACSD, pp. 119–127. IEEE, Los Alamitos (2009)
Uchitel, S., Chechik, M.: Merging partial behavioural models. In: Proc. of FSE 2004, pp. 43–52. ACM, New York (2004)
Huth, M., Jagadeesan, R., Schmidt, D.A.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 155–169. Springer, Heidelberg (2001)
Godefroid, P., Huth, M., Jagadeesan, R.: Abstraction-based model checking using modal transition systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 426–440. Springer, Heidelberg (2001)
Nanz, S., Nielson, F., Nielson, H.R.: Modal abstractions of concurrent behaviour. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 159–173. Springer, Heidelberg (2008)
Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: LICS, pp. 108–117. IEEE Computer Society, Los Alamitos (1990)
Fecher, H., Steffen, M.: Characteristic mu-calculus formulas for underspecified transition systems. ENTCS 128(2), 103–116 (2005)
Fecher, H., Schmidt, H.: Comparing disjunctive modal transition systems with an one-selecting variant. J. of Logic and Alg. Program. 77(1-2), 20–39 (2008)
Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: EXPTIME-complete decision problems for mixed and modal specifications. In: 15th International Workshop on Expressiveness in Concurrency (2008)
Beneš, N., Křetínský, J., Larsen, K., Srba, J.: On determinism in modal transition systems. Theoretical Computer Science 410(41), 4026–4043 (2009)
Juhl, L., Larsen, K.G., Srba, J.: Introducing modal transition systems with weight intervals (submitted)
Bruns, G., Godefroid, P.: Generalized model checking: Reasoning about partial state spaces. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 168–182. Springer, Heidelberg (2000)
Godefroid, P., Piterman, N.: LTL generalized model checking revisited. In: Jones, N.D., Müller-Olm, M. (eds.) VMCAI 2009. LNCS, vol. 5403, pp. 89–104. Springer, Heidelberg (2009)
Uchitel, S., Brunet, G., Chechik, M.: Synthesis of partial behavior models from properties and scenarios. IEEE Trans. Software Eng. 35(3), 384–406 (2009)
D’Ippolito, N., Fischbein, D., Chechik, M., Uchitel, S.: MTSA: The modal transition system analyser. In: Proc. of ASE 2008, pp. 475–476. IEEE, Los Alamitos (2008)
Beneš, N., Černá, I., Křetínský, J.: Disjunctive modal transition systems and generalized LTL model checking. Technical report FIMU-RS-2010-12, Faculty of Informatics, Masaryk University, Brno (2010)
Beneš, N., Křetínský, J.: Process algebra for modal transition systemses. In: MEMICS. OASICS, vol. 16, pp. 9–18. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2010)
Beneš, N., Křetínský, J., Larsen, K.G., Srba, J.: Checking thorough refinement on modal transition systems is EXPTIME-complete. In: Leucker, M., Morgan, C. (eds.) ICTAC 2009. LNCS, vol. 5684, pp. 112–126. Springer, Heidelberg (2009)
Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57. IEEE, Los Alamitos (1977)
Chaki, S., Clarke, E.M., Ouaknine, J., Sharygina, N., Sinha, N.: State/event-based software model checking. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 128–147. Springer, Heidelberg (2004)
Godefroid, P., Jagadeesan, R.: Automatic abstraction using generalized model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 137–151. Springer, Heidelberg (2002)
Godefroid, P., Jagadeesan, R.: On the expressiveness of 3-valued models. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 206–222. Springer, Heidelberg (2002)
Pnueli, A., Rosner, R.: On the synthesis of an asynchronous reactive module. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 652–671. Springer, Heidelberg (1989)
Dams, D., Namjoshi, K.S.: Automata as abstractions. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 216–232. Springer, Heidelberg (2005)
Alur, R., Torre, S.L.: Deterministic generators and games for LTL fragments. ACM Trans. Comput. Log. 5(1), 1–25 (2004)
Piterman, N., Pnueli, A.: Faster solution of rabin and streett games. In: Proceedings of LICS 2006, pp. 275–284. IEEE press, Los Alamitos (2006)
Baier, C., Katoen, J.P.: Principles of model checking. MIT Press, Cambridge (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beneš, N., Černá, I., Křetínský, J. (2011). Modal Transition Systems: Composition and LTL Model Checking. In: Bultan, T., Hsiung, PA. (eds) Automated Technology for Verification and Analysis. ATVA 2011. Lecture Notes in Computer Science, vol 6996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24372-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-24372-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24371-4
Online ISBN: 978-3-642-24372-1
eBook Packages: Computer ScienceComputer Science (R0)