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Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.

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References

  1. Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. Logic Comput. 4(3), 217–247 (1994). Revised version of Max-Planck-Institut für Informatik Technical report, MPI-I-91-208 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bachmair, L., Ganzinger, H.: Ordered chaining calculi for first-order theories of transitive relations. J. ACM 45(6), 1007–1049 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baeten, J.C.M., Bergstra, J.A., Klop, J., Weijland, W.P.: Term-rewriting systems with rule priorities. Theor. Comput. Sci. 67(2&3), 283–301 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baumgartner, P., Fuchs, A., Tinelli, C.: Implementing the model evolution calculus. Int. J. Artif. Intell. Tools 15(1), 21–52 (2006)

    Article  MATH  Google Scholar 

  5. Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 350–364. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45085-6_32

    Chapter  Google Scholar 

  6. Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007). http://www.grappa.univ-lille3.fr/tata. Accessed 12 Oct 2007

  7. Goubault-Larrecq, J.: Deciding \(\cal{H}_1\) by resolution. Inf. Process. Lett. 95(3), 401–408 (2005)

    Article  MATH  Google Scholar 

  8. Jacquemard, F., Meyer, C., Weidenbach, C.: Unification in extensions of shallow equational theories. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 76–90. Springer, Heidelberg (1998). doi:10.1007/BFb0052362

    Chapter  Google Scholar 

  9. Korovin, K.: iProver – an instantiation-based theorem prover for first-order logic (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195, pp. 292–298. Springer, Heidelberg (2008). doi:10.1007/978-3-540-71070-7_24

    Chapter  Google Scholar 

  10. Korovin, K.: Inst-Gen – a modular approach to instantiation-based automated reasoning. In: Voronkov, A., Weidenbach, C. (eds.) Programming Logics. LNCS, vol. 7797, pp. 239–270. Springer, Heidelberg (2013). doi:10.1007/978-3-642-37651-1_10

    Chapter  Google Scholar 

  11. Kovács, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_1

    Chapter  Google Scholar 

  12. Seidl, H., Reuß, A.: Extending H1-clauses with disequalities. Inf. Process. Lett. 111(20), 1007–1013 (2011)

    Article  MATH  Google Scholar 

  13. Seidl, H., Reuß, A.: Extending \({\cal{H}_1}\)-clauses with path disequalities. In: Birkedal, L. (ed.) FoSSaCS 2012. LNCS, vol. 7213, pp. 165–179. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28729-9_11

    Google Scholar 

  14. Seidl, H., Verma, K.N.: Cryptographic protocol verification using tractable classes of horn clauses. In: Reps, T., Sagiv, M., Bauer, J. (eds.) Program Analysis and Compilation, Theory and Practice. LNCS, vol. 4444, pp. 97–119. Springer, Heidelberg (2007). doi:10.1007/978-3-540-71322-7_5

    Chapter  Google Scholar 

  15. Slaney, J.K., Surendonk, T.: Combining finite model generation with theorem proving: problems and prospects. In: Baader, F., Schulz, K.U. (eds.), Frontiers of Combining Systems, First International Workshop FroCoS 1996, Munich, Germany, March 26-29, 1996, Proceedings, vol. 3. Applied Logic Series, pp. 141–155. Kluwer Academic Publishers (1996)

    Google Scholar 

  16. Suda, M., Weidenbach, C., Wischnewski, P.: On the saturation of YAGO. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 441–456. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14203-1_38

    Chapter  Google Scholar 

  17. Sutcliffe, G.: The TPTP problem library and associated infrastructure: the FOF and CNF Parts, v3.5.0. J. Autom. Reasoning 43(4), 337–362 (2009)

    Article  MATH  Google Scholar 

  18. Teucke, A., Weidenbach, C.: First-order logic theorem proving and model building via approximation and instantiation. In: Lutz, C., Ranise, S. (eds.) FroCoS 2015. LNCS (LNAI), vol. 9322, pp. 85–100. Springer, Cham (2015). doi:10.1007/978-3-319-24246-0_6

    Chapter  Google Scholar 

  19. Teucke, A., Weidenbach, C.: Ordered resolution with straight dismatching constraints. In: Fontaine, P., Schulz, S., Urban, J. (eds.) Proceedings of the 5th Workshop on Practical Aspects of Automated Reasoning Co-located with International Joint Conference on Automated Reasoning (IJCAR 2016), Coimbra, Portugal, 2 July 2016, vol. 1635. CEUR Workshop Proceedings, pp. 95–109 (2016). CEUR-WS.org

  20. Teucke, A., Weidenbach, C.: Decidability of the monadic shallow linear first-order fragment with straight dismatching constraints (2017). http://arxiv.org/abs/1703.02837

  21. Voronkov, A.: AVATAR: the architecture for first-order theorem provers. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 696–710. Springer, Cham (2014). doi:10.1007/978-3-319-08867-9_46

    Google Scholar 

  22. Weidenbach, C.: Towards an automatic analysis of security protocols in first-order logic. CADE 1999. LNCS, vol. 1632, pp. 314–328. Springer, Heidelberg (1999). doi:10.1007/3-540-48660-7_29

    Chapter  Google Scholar 

  23. Weidenbach, C., Dimova, D., Fietzke, A., Kumar, R., Suda, M., Wischnewski, P.: SPASS version 3.5. In: Schmidt, R.A. (ed.) CADE 2009. LNCS (LNAI), vol. 5663, pp. 140–145. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02959-2_10

    Chapter  Google Scholar 

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Acknowledgements

We thank the reviewers as well as Konstantin Korovin and Giles Reger for a number of important remarks.

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Authors and Affiliations

  1. Max-Planck Institut für Informatik, Saarland Informatics Campus, 66123, Saarbrücken, Germany

    Andreas Teucke & Christoph Weidenbach

  2. Graduate School of Computer Science, Saarbrücken, Germany

    Andreas Teucke

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  1. Andreas Teucke
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  2. Christoph Weidenbach
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Correspondence to Andreas Teucke .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Teucke, A., Weidenbach, C. (2017). Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_13

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63045-8

  • Online ISBN: 978-3-319-63046-5

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