On Local Reasoning in Verification

  • Carsten Ihlemann
  • Swen Jacobs
  • Viorica Sofronie-Stokkermans
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4963)


We present a general framework which allows to identify complex theories important in verification for which efficient reasoning methods exist. The framework we present is based on a general notion of locality. We show that locality considerations allow us to obtain parameterized decidability and complexity results for many (combinations of) theories important in verification in general and in the verification of parametric systems in particular. We give numerous examples; in particular we show that several theories of data structures studied in the verification literature are local extensions of a base theory. The general framework we use allows us to identify situations in which some of the syntactical restrictions imposed in previous papers can be relaxed.


Free Variable Function Symbol Local Extension Ground Term Total Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Burmeister, P.: A Model Theoretic Oriented Approach to Partial Algebras: Introduction to Theory and Application of Partial Algebras, Part I. In: Mathematical Research, vol. 31, Akademie-Verlag, Berlin (1986)Google Scholar
  3. 3.
    Burris, S.: Polynomial time uniform word problems. Mathematical Logic Quarterly 41, 173–182 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Faber, J., Jacobs, S., Sofronie-Stokkermans, V.: Verifying CSP-OZ-DC specifications with complex data types and timing parameters. In: Davies, J., Gibbons, J. (eds.) IFM 2007. LNCS, vol. 4591, pp. 233–252. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Ganzinger, H.: Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems. In: Proc. 16th IEEE Symposium on Logic in Computer Science (LICS 2001), pp. 81–92. IEEE Computer Society Press, Los Alamitos (2001)CrossRefGoogle Scholar
  6. 6.
    Ganzinger, H., Sofronie-Stokkermans, V., Waldmann, U.: Modular proof systems for partial functions with Evans equality. Information and Computation 204(10), 1453–1492 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Deciding extensions of the theory of arrays by integrating decision procedures and instantiation strategies. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 177–189. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Givan, R., McAllester, D.: New results on local inference relations. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR 1992), pp. 403–412. Morgan Kaufmann, San Francisco (1992)Google Scholar
  9. 9.
    Givan, R., McAllester, D.A.: Polynomial-time computation via local inference relations. ACM Transactions on Computational Logic 3(4), 521–541 (2002)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Jacobs, S., Sofronie-Stokkermans, V.: Applications of hierarchical reasoning in the verification of complex systems. Electronic Notes in Theoretical Computer Science 174(8), 39–54 (2007)CrossRefGoogle Scholar
  11. 11.
    McAllester, D.: Automatic recognition of tractability in inference relations. Journal of the Association for Computing Machinery 40(2), 284–303 (1993)zbMATHMathSciNetGoogle Scholar
  12. 12.
    McPeak, S., Necula, G.C.: Data structure specifications via local equality axioms. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 476–490. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Sofronie-Stokkermans, V.: Hierarchic reasoning in local theory extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 219–234. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Sofronie-Stokkermans, V.: Interpolation in local theory extensions. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 235–250. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Sofronie-Stokkermans, V.: Hierarchical and modular reasoning in complex theories: The case of local theory extensions. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS (LNAI), vol. 4720, pp. 47–71. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Sofronie-Stokkermans, V., Ihlemann, C.: Automated reasoning in some local extensions of ordered structures. In: Proc. of ISMVL-2007, IEEE Computer Society Press, Los Alamitos (2007), Google Scholar
  17. 17.
    Sofronie-Stokkermans, V., Ihlemann, C., Jacobs, S.: Local theory extensions, hierarchical reasoning and applications to verification. In: Dagstuhl Seminar Proceedings 07401,,

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Carsten Ihlemann
    • 1
  • Swen Jacobs
    • 1
  • Viorica Sofronie-Stokkermans
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations