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A logical characterization for linear higher-order processes

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Abstract

Modal logic characterization in a higher-order setting is usually not a trivial task because higher-order process-passing is quite different from first-order name-passing. We study the logical characterization of higher-order processes constrained by linearity. Linearity respects resource-sensitiveness and does not allow processes to duplicate themselves arbitrarily. We provide a modal logic that characterizes linear higher-order processes, particularly the bisimulation called local bisimulation over them. More importantly, the logic has modalities for higher-order actions downscaled to resembling first-order ones in Hennessy-Milner logic, based on a formulation exploiting the linearity of processes.

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References

  1. Milner R. Communication and concurrency [M]. New Jersey: Prentice Hall, 1989.

    Google Scholar 

  2. Milner R, Parrow J, Walker D. A calculus of mobile processes [J]. Information and Computation, 1992, 100(1): 1–77.

    Article  MATH  MathSciNet  Google Scholar 

  3. Sangiorgi D, Walker D. The π-calculus: A theory of mobile processes [M]. Cambridge: Cambridge Universtity Press, 2001.

    Google Scholar 

  4. Thomsen B. Calculi for higher order communicating systems [D]. London: Department of Computing, Imperial College, 1990.

    Google Scholar 

  5. Sangiorgi D. Expressing mobility in process algebras: First-order and higher-order paradigms [D]. Edinburgh: School of Informatics, University of Edinburgh, 1992.

    Google Scholar 

  6. Xu Xian. On the bisimulation theory and axiomatization of higher-order process calculi [D]. Shanghai: Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 2008 (in Chinese).

    Google Scholar 

  7. Lanese I, Pérez J A, Sangiorgi D, et al. On the expressiveness of polyadic and synchronous communication in higher-order process calculi [C]//Proceedings of ICALP 2010. New York: Springer-Verlag, 2010:442–453.

    Google Scholar 

  8. Lanese I, Pérez J A, Sangiorgi D, et al. On the expressiveness and decidability of higher-order process calculi[J]. Information and Computation, 2011, 209(2): 198–226.

    Article  MATH  MathSciNet  Google Scholar 

  9. Giusto C D, Pérez J A, Zavattaro G. On the expressiveness of forwarding in higher-order communication [C]//Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing (ICTAC’ 09). New York: Springer-Verlag, 2009: 155–169.

    Google Scholar 

  10. Xu X. Distinguishing and relating higher-order and first-order processes by expressiveness [J]. Acta Informatica, 2012, 49: 445–484.

    Article  MATH  MathSciNet  Google Scholar 

  11. Yuan Wen-jie, Ying Shi, Wu Ke-jia, et al. Formal description of the evolving reflective requirements specification with π-calculus [J]. Computer Engineering and Science, 2010, 32(6): 146–154 (in Chinese).

    Google Scholar 

  12. You Tao, Du Cheng-lie, Wang Wei, et al. A new component-based real-time system based on timed high-order(THO) calculus [J]. Journal of Northwestern Polytechnical University, 2009, 27(6): 6–11 (in Chinese).

    Google Scholar 

  13. Li Chang-yun, Li Gan-sheng, He Pin-jie. A formal dynamic architecture description language [J]. Journal of Software, 2006, 17(6): 1349–1359 (in Chinese).

    Article  Google Scholar 

  14. Zhan Nai-jun. On timed high-order calculus and its completeness [J]. Science in China: E Series, 2001, 31(1): 71–85 (in Chinese).

    Google Scholar 

  15. Fu Y. Checking equivalence for higher order processes [R]. Shanghai: BASICS, Shanghai Jiao Tong University, 2005.

    Google Scholar 

  16. Xu X. On bisimulation theory in linear higher-order π-calculus [J]. Transactions on Petri Nets and Other Models of Concurrency III, 2009, 5800: 244–274.

    Article  Google Scholar 

  17. Sangiorgi D. Bisimulation for higher-order process calculi [J]. Information and Computation, 1996, 131(2): 141–178.

    Article  MATH  MathSciNet  Google Scholar 

  18. Parrow J, Sangiorgi D. Algebraic theories for name-passing calculi [J]. Information and Computation, 1995, 120: 174–197.

    Article  MATH  MathSciNet  Google Scholar 

  19. Sangiorgi D. A theory of bisimulation for π-calculus [J]. Acta Informatica, 1996, 33(1): 69–97.

    Article  MATH  MathSciNet  Google Scholar 

  20. van Benthem J, van Eijck J, Stebletsova V. Modal logic, transition systems and processes [J]. Journal of Logic and Computation, 1994, 4(5): 811–855.

    Article  MATH  MathSciNet  Google Scholar 

  21. Henessy M, Milner R. Algebraic laws for nondeterminism and concurrency[J]. Journal of the ACM, 1985, 32: 137–161.

    Article  Google Scholar 

  22. Milner R, Parrow J, Walker D. Modal logics for mobile processes [J]. Theoretical Computer Science, 1993, 114(1): 149–171.

    Article  MATH  MathSciNet  Google Scholar 

  23. Stirling C. Modal logics for communicating systems [J]. Theoretical Computer Science, 1987, 49: 311–347.

    Article  MATH  MathSciNet  Google Scholar 

  24. Cleaveland R, Parrow J, Steffen B. The concurrency workbench: A semantics-based tool for the verification of concurrent systems [J]. ACM Transactions on Programming Lnaguages and Systems, 1993, 15(1): 36–72.

    Article  Google Scholar 

  25. Amadio R, Dam M. Reasoning about higher-order processes [C]//Proceedings of TAPSOFT’95. New York: Springer-Verlag, 1995: 202–216.

    Google Scholar 

  26. Thomsen B. Plain CHOCS, a second generation calculus for higher-order processes [J]. Acta Informatica, 1993, 30(1): 1–59.

    Article  MATH  MathSciNet  Google Scholar 

  27. Baldamus M, Dingel J. Modal characterization of weak bisimulation for higher-order processes [C]//Proceedings of TAPSOFT’97. New York: Springer-Verlag, 1997: 285–296.

    Google Scholar 

  28. Koutavas V, Hennessy M. First-order reasoning for higher-order concurrency [J]. Computer Languages, Systems and Structures, 2012, 38(3): 242–277.

    Article  MATH  Google Scholar 

  29. Jeffrey A, Rathke J. Contextual equivalence for higher-order π-calculus revisited [J]. Logical Methods in Computer Science, 2005, 1(1): 1–20.

    Article  MathSciNet  Google Scholar 

  30. Sangiorgi D, Kobayashi N, Sumii E. Environmental bisimulations for higher-order languages [J]. ACM Transactions on Programming Languages and Systems, 2011, 33(1): 1–10.

    Article  Google Scholar 

  31. Caires L, Cardelli L. A spatial logic for concurrency: Part I [J]. Information and Computation, 2003, 186(2): 194–235.

    Article  MATH  MathSciNet  Google Scholar 

  32. Caires L, Cardelli L. A spatial logic for concurrency: Part II [J]. Theoretical Computer Science, 2004, 322(3): 517–565.

    Article  MATH  MathSciNet  Google Scholar 

  33. Cao Z. A spatial logical characterisation of context bisimulation [C]//Proceeding of ASIAN2006. New York: Springer-Verlag, 2006: 232–240.

    Google Scholar 

  34. Cao Z. Modal ZIA, modal refinement relation and logical characterization [C]//Proceedings of SEKE2012. California: World Scientific Publishing Co., 2012: 525–530.

    Google Scholar 

  35. Cao Z. Reducing higher order π-calculus to spatial logics [C]//Proceedings of COMPUTATION TOOLS 2013. Valencia: Xpert Publishing Services, 2013: 44–53.

    Google Scholar 

  36. Lago U D, Martini S, Sangiorgi D. Light logics and higher-order processes [C]//Proceedings of Workshop on Expressiveness in Concurrency 2010 (EXPRESS 2010). Sydney: EPTCS, 2010: 46–60.

    Google Scholar 

  37. Kobayashi N, Yonezawa A. Higher-order concurrent linear logic programming [C]//Proceedings of International Workshop TPPP’ 94. New York: Springer-Verlag, 1994: 137–166.

    Google Scholar 

  38. Frauenstein T, Baldamus M, Glas R. Congruence proofs for weak bisimulation on higher-order processes: Results for typed ω-order calculi [R]. Berlin: Berlin University of Technology, Computer Science Department, 1996.

    Google Scholar 

  39. Barendregt H P. The lambda calculus: Its syntax and semantics [M]. [s.l.]: North-Holland, 1984.

    Google Scholar 

  40. Barras B, Boutin S, Cornes C, et al. The Coq proof assistant (reference manual) [R]. [s.l.]: The Coq Development team, 2012.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Technology, East China University of Science and Technology, Shanghai, 200237, China

    Xian Xu  (徐 贤)

  2. Laboratory of Basic Study In Computing Science, MOE-MS Key Laboratory for Intelligent Computing and Intelligent Systems, Department of Computer Science and Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Huan Long  (龙 环)

Authors
  1. Xian Xu  (徐 贤)
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  2. Huan Long  (龙 环)
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Corresponding author

Correspondence to Xian Xu  (徐 贤).

Additional information

Foundation item: the National Natural Science Foundation of China (Nos. 61202023, 61261130589 and 61173048), the PACE Project (No. 12IS02001), and the Specialized Research Fund for the Doctoral Program of Higher Edueation of China (No. 20120073120031)

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Xu, X., Long, H. A logical characterization for linear higher-order processes. J. Shanghai Jiaotong Univ. (Sci.) 20, 185–194 (2015). https://doi.org/10.1007/s12204-014-1554-y

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  • DOI: https://doi.org/10.1007/s12204-014-1554-y

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