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Formal Language Constrained Reachability and Model Checking Propositional Dynamic Logics

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Book cover Reachability Problems (RP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6945))

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Abstract

We show interreducibility under (Turing) reductions of low polynomial degree between three families of problems parametrised by classes of formal languages: the problem of reachability in a directed graph constrained by a formal language, the problem of deciding whether or not the intersection of a language of some class with a regular language is empty, and the model checking problem for Propositional Dynamic Logic over some class of formal languages. This allows several decidability and complexity results to be transferred, mainly from the area of formal languages to the areas of modal logics and formal language constrained reachability.

The European Research Council has provided financial support under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no 259267.

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References

  1. Aho, A.V.: Indexed grammars - an extension of context-free grammars. J. ACM 15(4), 647–671 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Proc. 36th Ann. ACM Symp. on Theory of Computing (STOC 2004), pp. 202–211. ACM Press, New York (2004)

    Google Scholar 

  3. Baader, F., Lutz, C., Turhan, A.-Y.: Small is again beautiful in description logics. KI – Künstliche Intelligenz (2010) (to appear)

    Google Scholar 

  4. Bar-Hillel, Y., Perles, M., Shamir, E.: On formal properties of simple phrase structure grammars. Zeitschrift für Phonologie, Sprachwissenschaft und Kommunikationsforschung 14, 113–124 (1961)

    MathSciNet  MATH  Google Scholar 

  5. Barrett, C., Jacob, R., Marathe, M.: Formal-language-constrained path problems. SIAM Journal on Computing 30(3), 809–837 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  7. Fähndrich, M., Rehof, J.: Type-based flow analysis and context-free language reachability. Mathematical Structures in Computer Science 18(5), 823–894 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18, 194–211 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gazdar, G.: Applicability of indexed grammars to natural languages. In: Reyle, U., Rohrer, C. (eds.) Natural Language Parsing and Linguistic Theories, pp. 69–94. Reidel, Dordrecht (1988)

    Chapter  Google Scholar 

  10. De Giacomo, G., Lenzerini, M.: Boosting the correspondence between description logics and propositional dynamic logics. In: Proc. of the 12th National Conference on Artificial Intelligence (AAAI 1994), pp. 205–212. AAAI-Press/The MIT-Press (1994)

    Google Scholar 

  11. Harel, D., Kaminsky, M.: Strengthened results on nonregular PDL. Technical Report MCS99-13, Weizmann Institute of Science, Faculty of Mathematics and Computer Science (1999)

    Google Scholar 

  12. Harel, D., Pnueli, A., Stavi, J.: Propositional dynamic logic of nonregular programs. Journal of Computer and System Sciences 26(2), 222–243 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  13. Harel, D., Raz, D.: Deciding properties of nonregular programs. SIAM J. Comput. 22(4), 857–874 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Harel, D., Singerman, E.: More on nonregular PDL: Finite models and Fibonacci-like programs. Information and Computation 128(2), 109–118 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hunt, H.B.: On the time and tape complexity of languages I. In: ACM (ed.) Conf. Rec. of 5th Annual ACM Symp. on Theory of Computing (STOC 1973), pp. 10–19. ACM Press, New York (1973)

    Google Scholar 

  16. Landweber, P.S.: Three theorems on phrase structure grammars of type 1. Inform. and Control 6, 131–136 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lange, M.: Alternating context-free languages and linear time μ-calculus with sequential composition. In: Proc. 9th Workshop on Expressiveness in Concurrency (EXPRESS 2002). ENTCS, vol. 68.2, pp. 71–87. Elsevier, Amsterdam (2002)

    Google Scholar 

  18. Lange, M.: Model checking propositional dynamic logic with all extras. Journal of Applied Logic 4(1), 39–49 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Löding, C., Lutz, C., Serre, O.: Propositional dynamic logic with recursive programs. J. Log. Algebr. Program 73(1-2), 51–69 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL-recognition. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 422–435. Springer, Heidelberg (1980)

    Chapter  Google Scholar 

  21. Moriya, E.: A grammatical characterization of alternating pushdown automata. TCS 67(1), 75–85 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Nitta, N., Seki, H., Takata, Y.: Security verification of programs with stack inspection. In: SACMAT, pp. 31–40 (2001)

    Google Scholar 

  23. Okhotin, A.: Conjunctive grammars. Journal of Automata, Languages and Combinatorics 6(4), 519–535 (2001)

    MathSciNet  MATH  Google Scholar 

  24. Okhotin, A.: Boolean grammars. Information and Computation 194(1), 19–48 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  25. Prendinger, H., Schurz, G.: Reasoning about action and change. A dynamic logic approach. Journal of Logic, Language and Information 5(2), 209–245 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  26. Reps, T.: Shape analysis as a generalized path problem. In: Proc. ACM SIGPLAN Symp. on Partial Evaluation and Semantics-Based Program Manipulation, pp. 1–11 (1995)

    Google Scholar 

  27. Reps, T.W.: Program analysis via graph reachability. Information & Software Technology 40(11-12), 701–726 (1998)

    Article  Google Scholar 

  28. Tanaka, S., Kasai, T.: The emptiness problem for indexed language is exponential-time complete. Systems and Computers in Japan 17(9), 29–37 (2007)

    Article  MathSciNet  Google Scholar 

  29. La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: Proc. 22nd Conf. on Logic in Computer Science (LICS 2007), pp. 161–170. IEEE, Los Alamitos (2007)

    Google Scholar 

  30. Vijay-Shanker, K., Weir, D.J.: The equivalence of four extensions of context-free grammars. Mathematical Systems Theory 27, 27–511 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Munich, Germany

    Roland Axelsson

  2. School of Electr. Eng. and Computer Science, University of Kassel, Germany

    Martin Lange

Authors
  1. Roland Axelsson
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  2. Martin Lange
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Scienze dell’Informazione, Università di Genova, via Dodecaneso 35, 16146, Genoa, Italy

    Giorgio Delzanno

  2. Department of Computer Science, University of Liverpool, Ashton St, Ashton Building, L69 3BX, Liverpool, UK

    Igor Potapov

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Axelsson, R., Lange, M. (2011). Formal Language Constrained Reachability and Model Checking Propositional Dynamic Logics. In: Delzanno, G., Potapov, I. (eds) Reachability Problems. RP 2011. Lecture Notes in Computer Science, vol 6945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24288-5_6

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  • DOI: https://doi.org/10.1007/978-3-642-24288-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24287-8

  • Online ISBN: 978-3-642-24288-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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