Theorem Proving Based on Proof Scores for Rewrite Theory Specifications of OTSs

  • Kazuhiro Ogata
  • Kokichi Futatsugi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8373)


We have intensively used proof scores to theorem prove that equational theory specifications of observational transition systems (OTSs) have properties. The paper describes a way to theorem prove that rewrite theory specifications of OTSs have invariant properties by proof score writing. The method may achieve a more faithfully seamless integration of model checking and theorem proving because no translation is needed for system specifications. The Lowe’s modification (NSLPK) of NSPK authentication protocol is used to describe the method.


(bounded) model checking proof score rewrite theory specification search theorem proving 


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  1. 1.
    Ogata, K., Kurihara, S., Inari, M., Doi, N.: The design and implementation of HoME. In: PLDI 1992, pp. 44–54 (1992)Google Scholar
  2. 2.
    Ogata, K., Doi, N.: Object allocation and dynamic compilation in MultithreadSmalltalk. In: 9th SAC, pp. 452–456 (1994)Google Scholar
  3. 3.
    Ogata, K., Ohhara, K., Futatsugi, K.: TRAM: An abstract machine for order-sorted conditional term rewriting systems. In: Comon, H. (ed.) RTA 1997. LNCS, vol. 1232, pp. 335–338. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Ogata, K., Kondo, M., Ioroi, S., Futatsugi, K.: Design and implementation of Parallel TRAM. In: Lengauer, C., Griebl, M., Gorlatch, S. (eds.) Euro-Par 1997. LNCS, vol. 1300, pp. 1209–1216. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Ogata, K., Hirata, H., Ioroi, S., Futatsugi, K.: Experimental implementation of Parallel TRAM on massively parallel computer. In: Pritchard, D., Reeve, J. (eds.) Euro-Par 1998. LNCS, vol. 1470, pp. 846–851. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Ogata, K., Futatsugi, K.: Specification and verification of some classical mutual exclusion algorithms with CafeOBJ. In: OBJ/CafeOBJ/Maude Workshop at FM 1999, pp. 159–177 (1999)Google Scholar
  7. 7.
    Ogata, K., Futatsugi, K.: Proof scores in the OTS/CafeOBJ method. In: Najm, E., Nestmann, U., Stevens, P. (eds.) FMOODS 2003. LNCS, vol. 2884, pp. 170–184. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Ogata, K., Futatsugi, K.: Some tips on writing proof scores in the OTS/CafeOBJ method. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.) Goguen Festschrift. LNCS, vol. 4060, pp. 596–615. Springer, Heidelberg (2006)Google Scholar
  9. 9.
    Goguen, J., Malcolm, G.: A hidden agenda. TCS 245, 55–101 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Diaconescu, R., Futatsugi, K.: Behavioural coherence in object-oriented algebraic specification. J. UCS 6, 74–95 (2000)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Chandy, K.M., Misra, J.: Parallel Program Design: A Foundation. Addison-Wesley (1988)Google Scholar
  12. 12.
    Diaconescu, R., Futatsugi, K.: CafeOBJ report. AMAST Series in Computing 6. World Scientific (1998)Google Scholar
  13. 13.
    Ogata, K., Futatsugi, K.: Formal verification of the MCS list-based queuing lock. In: Thiagarajan, P.S., Yap, R. (eds.) ASIAN 1999. LNCS, vol. 1742, pp. 281–293. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Ogata, K., Futatsugi, K.: Formal analysis of Suzuki&Kasami distributed mutual exclusion algorithm. In: Jacobs, B., Rensink, A. (eds.) Formal Methods for Open Object-Based Distributed Systems V. IFIP, vol. 81, pp. 181–195. Springer, Heildelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Xiang, J., Ogata, K., Futatsugi, K.: Formal fault tree analysis of state transition systems. In: 5th QSIC, pp. 124–131 (2005)Google Scholar
  16. 16.
    Kong, W., Ogata, K., Futatsugi, K.: Specification and verification of workflows with RBAC mechanism and SoD constraints. IJSEKE 17, 3–32 (2007)Google Scholar
  17. 17.
    Ogata, K., Futatsugi, K.: Formal analysis of the bakery protocol with consideration of nonatomic reads and writes. In: Liu, S., Maibaum, T., Araki, K. (eds.) ICFEM 2008. LNCS, vol. 5256, pp. 187–206. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Kong, W., Ogata, K., Futatsugi, K.: Towards reliable e-government systems with the OTS/CafeOBJ method. IEICE Transactions E93-D, 974–984 (2010)CrossRefGoogle Scholar
  19. 19.
    Ogata, K., Futatsugi, K.: Proof score approach to analysis of electronic commerce protocols. IJSEKE 20, 253–287 (2010)Google Scholar
  20. 20.
    Zhang, M., Ogata, K., Futatsugi, K.: Formalization and verification of behavioral correctness of dynamic software updates. In: 2nd VSSE. ENTCS, vol. 294, pp. 12–23 (2013)Google Scholar
  21. 21.
    Futatsugi, K., Goguen, J., Ogata, K.: Verifying design with proof scores. In: Meyer, B., Woodcock, J. (eds.) VSTTE 2005. LNCS, vol. 4171, pp. 277–290. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Futatsugi, K., Găină, D., Ogata, K.: Principles of proof scores in CafeOBJ. TCS 464, 90–112 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Ogata, K., Futatsugi, K.: Proof score approach to verification of liveness properties. IEICE Transactions E91-D, 2804–2817 (2008)CrossRefGoogle Scholar
  24. 24.
    Ogata, K., Futatsugi, K.: Modeling and verification of real-time systems based on equations. SCP 66, 162–180 (2007)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Ouranos, I., Ogata, K., Stefaneas, P.: Formal analysis of TESLA protocol in the Timed OTS/CafeOBJ method. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012, Part II. LNCS, vol. 7610, pp. 126–142. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  26. 26.
    Nakano, M., Ogata, K., Nakamura, M., Futatsugi, K.: Creme: An automatic invariant prover of behavioral specifications. IJSEKE 17, 783–804 (2007)Google Scholar
  27. 27.
    Găină, D., Futatsugi, K., Ogata, K.: Constructor-based logics. J. UCS 18, 90–112 (2012)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Găină, D., Zhang, M., Chiba, Y., Arimoto, Y.: Constructor-based inductive theorem prover. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 328–333. Springer, Heidelberg (2013)Google Scholar
  29. 29.
    Ogata, K., Nakano, M., Kong, W., Futatsugi, K.: Induction-guided falsification. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 114–131. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  30. 30.
    Ogata, K., Futatsugi, K.: A combination of forward & backward reachability analysis methods. In: Dong, J.S., Zhu, H. (eds.) ICFEM 2010. LNCS, vol. 6447, pp. 501–517. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  31. 31.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  32. 32.
    Kong, W., Ogata, K., Futatsugi, K.: Model-checking observational transition system with Maudea. In: 20th ITC-CSCC, pp. 5–6 (2005)Google Scholar
  33. 33.
    Ogata, K., Kong, W., Futatsugi, K.: Falsification of OTSs by searches of bounded reachable state spaces. In: 18th SEKE, pp. 440–445 (2006)Google Scholar
  34. 34.
    Kong, W., Ogata, K., Seino, T., Futatsugi, K.: A lightweight integration of theorem proving and model checking for system verification. In: 12th APSEC, pp. 59–66 (2005)Google Scholar
  35. 35.
    Nakamura, M., Kong, W., Ogata, K., Futatsugi, K.: A specification translation from behavioral specifications to rewrite specifications. IEICE Transactions E91-D, 1492–1503 (2008)CrossRefGoogle Scholar
  36. 36.
    Zhang, M., Ogata, K., Nakamura, M.: Translation of state machines from equational theories into rewrite theories with tool support. IEICE Transactions 94-D, 976–988 (2011)CrossRefGoogle Scholar
  37. 37.
    Zhang, M., Ogata, K.: Invariant-preserved transformation of state machines from equations into rewrite rules. In: 18th APSEC, pp. 511–516 (2012)Google Scholar
  38. 38.
    Lowe, G.: An attack on the Needham-Schroeder public-key authentication protocol. IPL 56, 131–133 (1995)CrossRefzbMATHGoogle Scholar
  39. 39.
    Needham, R.M., Schroeder, M.D.: Using encryption for authentication in large networks of computers. CACM 21, 993–999 (1978)CrossRefzbMATHGoogle Scholar
  40. 40.
    Dolev, D., Yao, A.C.: On the security of public key protocols. IEEE TIT IT-29, 198–208 (1983)MathSciNetzbMATHGoogle Scholar
  41. 41.
    Goguen, J., Winkler, T., Meseguer, J., Futatsugi, K., Jouannaud, J.P.: Introducing OBJ. In: Software Engineering with OBJ: Algebraic Specification in Action. Kluwer (2000)Google Scholar
  42. 42.
    Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational abstractions. TCS 403, 239–264 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Rocha, C., Meseguer, J.: Proving safety properties of rewrite theories. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 314–328. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  44. 44.
    Jouannaud, J.P., Kirchner, C., Kirchner, H.: Incremental construction of unification algorithms in equational theories. In: Diaz, J. (ed.) 10th ICALP. LNCS, vol. 154, pp. 361–373. Springer, Heidelberg (1983)Google Scholar
  45. 45.
    Ogata, K., Futatsugi, K.: Compositionally writing proof scores of invariants in the OTS/CafeOBJ method. J. UCS 19, 771–804 (2013)Google Scholar
  46. 46.
    Bae, K., Escobar, S., Meseguer, J.: Abstract logical model checking of infinite-state systems using narrowing. In: 24th RTA, pp. 81–96 (2013)Google Scholar
  47. 47.
    de Moura, L., Rueß, H., Sorea, M.: Bounded model checking and induction: From refutation to verification. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 14–26. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  48. 48.
    de Moura, L., Owre, S., Rueß, H., Rushby, J., Shankar, N., Sorea, M., Tiwari, A.: SAL 2. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 496–500. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  49. 49.
    Hennicker, R.: Context induction: A proof principle for behavioural abstractions. In: Miola, A. (ed.) DISCO 1990. LNCS, vol. 429, pp. 101–110. Springer, Heidelberg (1990)Google Scholar
  50. 50.
    Roşu, G., Lucanu, D.: Circular coinduction: A proof theoretical foundation. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 127–144. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Kazuhiro Ogata
    • 1
  • Kokichi Futatsugi
    • 1
  1. 1.School of Information ScienceJAISTJapan

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