Formal Aspects of Computing

, Volume 25, Issue 4, pp 503–541 | Cite as

HYPE: Hybrid modelling by composition of flows

  • Vashti Galpin
  • Luca Bortolussi
  • Jane Hillston
Original Article


Hybrid systems are manifest in both the natural and the engineered world, and their complex nature, mixing discrete control and continuous evolution, make it difficult to predict their behaviour. In recent years several process algebras for modelling hybrid systems have appeared in the literature, aimed at addressing this problem. These all assume that continuous variables in the system are modelled monolithically, often with differential equations embedded explicitly in the syntax of the process algebra expression. In HYPE an alternative approach is taken which offers finer-grained modelling with each flow or influence affecting a variable modelled separately. The overall behaviour then emerges as the composition of flows. In this paper we give a detailed account of the HYPE process algebra, its semantics, and its use for verification of systems. We establish both syntactic conditions (well-definedness) and operational restrictions (well-behavedness) to ensure reasonable behaviour in HYPE models. Furthermore we consider how the equivalence relation defined for HYPE relates to other relations previously proposed in the literature, demonstrating that our fine-grained approach leads to a more discriminating notion of equivalence. We present the HYPE model of a standard hybrid system example, both establishing that our approach can reproduce the previously obtained results and demonstrating how our compositional approach supports variations of the problem in a straightforward and flexible way.


Hybrid systems Process algebra Flows Compositionality Bisimulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AGLS06.
    Alur R, Grosu R, Lee I, Sokolsky O (2006) Compositional modeling and refinement for hierarchical hybrid systems. J Logic Algebraic Program 68: 105–128MathSciNetzbMATHCrossRefGoogle Scholar
  2. AGLT10.
    Akman OE, Guerriero ML, Loewe L, Troein C (2010) Complementary approaches to understanding the plant circadian clock. In: Proceedings of FBTC’10, EPTCS, vol 19, pp 1–19Google Scholar
  3. AHH96.
    Alur R, Henzinger TA, Ho P-H (1996) Automatic symbolic verification of embedded systems. IEEE Trans Softw Eng 22: 181–201CrossRefGoogle Scholar
  4. AMP+03.
    Antoniotti M, Mishra B, Piazza C, Policriti A, Simeoni M (2003) Modeling cellular behavior with hybrid automata: bisimulation and collapsing. In: Priami C (ed) Proceedings of CMSB 2003. LNCS, vol 2602, pp 57–74Google Scholar
  5. BGH10a.
    Bortolussi L, Galpin V, Hillston J (2010) HYPE with stochastic events. In: Proceedings of QAPL 2011, EPTCS, vol 57, pp 120–133Google Scholar
  6. BGH10b.
    Bortolussi L, Galpin V, Hillston J (2010) Modeling hybrid systems with stochastic events in HYPE. In: Proceedings of the 9th workshop on process algebra and stochastically timed activities (PASTA), pp 24–28Google Scholar
  7. BM05.
    Bergstra JA, Middelburg CA (2005) Process algebra for hybrid systems. Theor Comput Sci 335: 215–280MathSciNetzbMATHCrossRefGoogle Scholar
  8. BP08.
    Bortolusssi L, Policriti A (2008) Hybrid approximation of stochastic process algebras for systems biology. In: IFAC World Congress, Seoul, South Korea, July 2008Google Scholar
  9. BP09.
    Bortolussi L, Policriti A (2009) Hybrid semantics of stochastic programs with dynamic reconfiguration. In: Proceedings of COMPMOD 2009, EPTCS, vol 6, pp 63–76Google Scholar
  10. CBM08.
    Cuijpers PJL, Broenink JF, Mosterman PJ (2008) Constitutive hybrid processes: a process-algebraic semantics for hybrid bond graphs. Simulation 8: 339–358CrossRefGoogle Scholar
  11. CR03.
    Cuijpers PJL, Reniers MA (2003) Hybrid process algebra. Computer Science Reports CSR 03-07, Department of Computer Science, Eindhoven Technical UniversityGoogle Scholar
  12. CR05.
    Cuijpers PJL, Reniers MA (2005) Hybrid process algebra. J Logic Algebraic Program 62: 191–245MathSciNetzbMATHCrossRefGoogle Scholar
  13. Dav93.
    Davis MHA (1993) Markov models and optimization. Chapman & HallGoogle Scholar
  14. DGV96.
    Deshpande A, Göllü A, Varaiya P (1996) SHIFT: a formalism and a programming language for dynamic networks of hybrid automata. In: Antsaklis PJ, Kohn W, Nerode A, Sastry S (eds) Proceedings of hybrid systems IV. LNCS, vol 1273, pp 113–133Google Scholar
  15. DPP04.
    Dovier A, Piazza C, Policriti A (2004) An efficient algorithm for computing bisimulation. Theor Comput Sci 311: 221–256MathSciNetzbMATHCrossRefGoogle Scholar
  16. DT07.
    Davoren JM, Tabuada P (2007) On simulations and bisimulations of general flow systems. In: Bemporad A, Bicchi A, Buttazzo GC (eds) Proceedings of HSCC 2007. LNCS, vol 4416, pp 145–158Google Scholar
  17. EL00.
    Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335–338CrossRefGoogle Scholar
  18. Gal10.
    Galpin V (2010) Modelling a circadian clock with HYPE. In: Proceedings of the 9th workshop on process algebra and stochastically timed activities (PASTA), pp 92–98Google Scholar
  19. GBH09.
    Galpin V, Bortolussi L, Hillston J (2009) Hype: a process algebra for compositional flows and emergent behaviour. In: Bravetti M, Zavattaro G (eds) Proceedings of CONCUR 2009. LNCS, vol 5710. Springer, Berlin, pp 305–320Google Scholar
  20. GHB08.
    Galpin V, Hillston J, Bortolussi L (2008) HYPE applied to the modelling of hybrid biological systems. Electron Notes Theor Comput Sci 218: 33–51CrossRefGoogle Scholar
  21. GHB10.
    Galpin V, Hillston J, Bortolussi L (2010) A stochastic hybrid process algebra (poster). In: Models and logics for quantitative analysis (MLQA 2010), Edinburgh, July 2010Google Scholar
  22. GS02.
    Grosu R, Stauner T (2002) Modular and visual specification of hybrid systems: an introduction to HyCharts. Formal Methods Syst Des 21: 5–38zbMATHCrossRefGoogle Scholar
  23. Hen96.
    Henzinger TA (1996) The theory of hybrid automata. In: LICS, pp 278–292Google Scholar
  24. HH94.
    Henzinger TA, Ho P-H (1994) HYTECH: The Cornell HYbrid TECHnology Tool. In: Antsaklis PJ, Kohn W, Nerode A, Sastry S (eds) Hybrid systems. LNCS, vol 999. Springer, Berlin, pp 265–293Google Scholar
  25. Hil05.
    Hillston J (2005) Fluid flow approximation of PEPA models. In: Second international conference on the quantitative evaluation of systems (QEST 2005). IEEE Computer Society, pp 33–43Google Scholar
  26. HKPV95.
    Henzinger TA, Kopke PW, Puri A, and Varaiya P (1995) What’s decidable about hybrid automata? In: Proceedings of the twenty-seventh annual ACM symposium on theory of computing, STOC ’95, pp 373–382Google Scholar
  27. HTP05.
    Haghverdi E, Tabuada P, Pappas GJ (2005) Bisimulation relations for dynamical, control, and hybrid systems. Theor Comput Sci 342: 229–261MathSciNetzbMATHCrossRefGoogle Scholar
  28. Kha06.
    Khadim U (2006) A comparative study of process algebras for hybrid systems. Computer Science Report CSR 06-23, Technische Universiteit Eindhoven.
  29. Kha08.
    Khadim U (2008) Process algebras for hybrid systems: comparison and development. PhD thesis, IPA, Technische Universiteit EindhovenGoogle Scholar
  30. LPS00.
    Lafferriere G, Pappas GJ, Sastry S (2000) O-minimal hybrid systems. Math Control Signals Syst 13: 1–21MathSciNetzbMATHCrossRefGoogle Scholar
  31. Mil89.
    Milner R (1989) Communication and concurrency. Prentice HallGoogle Scholar
  32. MRG05.
    Mousavi MR, Reniers MA, Groote JF (2005) Notions of bisimulation and congruence formats for SOS with data. Inf Comput 200: 107–147MathSciNetzbMATHCrossRefGoogle Scholar
  33. Pay61.
    Paynter HM (1961) Analysis and design of engineering systems. MIT PressGoogle Scholar
  34. RRS03.
    Rönkkö M, Ravn AP, Sere K (2003) Hybrid action systems. Theor Comput Sci 290: 937–973zbMATHCrossRefGoogle Scholar
  35. RS03.
    Rounds WC, Song H (2003) The φ-calculus: a language for distributed control of reconfigurable embedded systems. In: Maler O, Pnueli A (eds) Proceedings of HSCC 2003. LNCS, vol 2623, pp 435–449Google Scholar
  36. TCT01.
    Tuffin B, Chen DS, Trivedi KS (2001) Comparison of hybrid systems and fluid stochastic Petri nets. Discrete Event Dyn Syst Theory Appl 11: 77–95MathSciNetzbMATHCrossRefGoogle Scholar
  37. TGH10.
    Tribastone M, Gilmore S, Hillston J (2010) Scalable differential analysis of process algebra models. IEEE Trans Softw Eng. doi: 10.1109/TSE.201082
  38. vBMR+06.
    van Beek DA, Man KL, Reniers MA, Rooda JE, Schiffelers RRH (2006) Syntax and consistent equation semantics of hybrid χ. J Logic Algebraic Program 68: 129–210zbMATHCrossRefGoogle Scholar
  39. vG90.
    van Glabbeek RJ (1990) The linear time-branching time spectrum (extended abstract). In: Proceedings of CONCUR 90. LNCS, vol 458. Springer, Berlin, pp 278–297Google Scholar

Copyright information

© British Computer Society 2011

Authors and Affiliations

  1. 1.Laboratory for Foundations of Computer Science, School of InformaticsUniversity of EdinburghEdinburghUK
  2. 2.Department of Mathematics and Computer ScienceUniversity of TriesteTriesteItaly

Personalised recommendations