Skip to main content
Springer Nature Link
Log in

Simulation Relations and Applications in Formal Methods

  • Chapter
  • First Online:
Principles of Systems Design

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13660))

  • 1082 Accesses

Abstract

We survey the research on application of equivalence checking to formal methods, with a particular focus on the notion of simulation and bisimulation as well as of modal refinement on modal transition systems. We discuss the algorithmic aspects of efficiently computing (bi)simulation relations, the extension to infinite state systems, and existing tool support. We then present results related to simulation and bisimulation checking on timed and hybrid systems and highlight the connections to automata theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    The original definition is given for transition systems with labeled states. Here we use an adaptation to labeled transitions.

References

  1. Abadi, M., Lamport, L.: The existence of refinement mappings. Theor. Comput. Sci. 82(2), 253–284 (1991). https://doi.org/10.1016/0304-3975(91)90224-P

  2. Abdulla, P.A., Holík, L., Kaati, L., Vojnar, T.: A uniform (bi-)simulation-based framework for reducing tree automata. Electron. Notes Theor. Comput. Sci. 251, 27–48 (2009). https://doi.org/10.1016/j.entcs.2009.08.026

  3. Aceto, L., Ingólfsdóttir, A., Larsen, K.G., Srba, J.: Reactive Systems: Modelling. Cambridge University Press, Specification and Verification (2007)

    Book  MATH  Google Scholar 

  4. Aceto, L., Ingólfsdóttir, A., Srba, J.: The algorithmics of bisimilarity. In: Advanced Topics in Bisimulation and Coinduction, Cambridge tracts in theoretical computer science, vol. 52, pp. 100–172. Cambridge University Press (2012)

    Google Scholar 

  5. Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Hybrid Systems. LNCS, vol. 736, pp. 209–229. Springer, Cham (1992). https://doi.org/10.1007/3-540-57318-6_30

  6. Alur, R., Dill, D.L.: Automata for modeling real-time systems. In: ICALP, LNCS, vol. 443, pp. 322–335. Springer, Cham (1990). https://doi.org/10.1007/BFb0032042

  7. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010--8

  8. Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC. pp. 202–211. ACM (2004). https://doi.org/10.1145/1007352.1007390

  9. Andersen, J.R., et al.: CAAL: concurrency workbench, Aalborg edition. In: ICTAC. LNCS, vol. 9399, pp. 573–582. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25150-9_33

  10. Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: 20 years of modal and mixed specifications. Bull. EATCS 95, 94–129 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: Complexity of decision problems for mixed and modal specifications. In: FOSSACS. LNCS, vol. 4962, pp. 112–126. Springer, Cham (2008). https://doi.org/10.1007/978-3-540-78499-9_9

  12. Antonik, A., Huth, M., Larsen, K.G., Nyman, U., Wasowski, A.: EXPTIME-complete decision problems for modal and mixed specifications. ENTCS 242(1), 19–33 (2009). https://doi.org/10.1016/j.entcs.2009.06.011

  13. Asarin, E., Maler, O., Pnueli, A.: Symbolic controller synthesis for discrete and timed systems. In: Hybrid Systems. LNCS, vol. 999, pp. 1–20. Springer, Cham (1994). https://doi.org/10.1007/3-540-60472-3_1

  14. Baier, C., Katoen, J.: Principles of Model Checking. MIT Press (2008)

    Google Scholar 

  15. Bauer, S.S., Juhl, L., Larsen, K.G., Srba, J., Legay, A.: A logic for accumulated-weight reasoning on multiweighted modal automata. In: TASE, pp. 77–84. IEEE Computer Society (2012). https://doi.org/10.1109/TASE.2012.9

  16. Benes, N., Křetínský, J., Larsen, K.G., Srba, J.: On determinism in modal transition systems. Theor. Comput. Sci. 410(41), 4026–4043 (2009). https://doi.org/10.1016/j.tcs.2009.06.009

  17. Beneš, N., Křetínský, J., Larsen, K.G., Møller, M.H., Srba, J.: Parametric modal transition systems. In: ATVA. LNCS, vol. 6996, pp. 275–289. Springer, Cham (2011). https://doi.org/10.1007/978-3-642-24372-1_20

  18. Beneš, N., Křetínský, J., Larsen, K.G., Srba, J.: Checking thorough refinement on modal transition systems is EXPTIME-complete. In: ICTAC. LNCS, vol. 5684, pp. 112–126. Springer, Cham (2009). https://doi.org/10.1007/978-3-642-03466-4_7

  19. Bensalem, S., Bouajjani, A., Loiseaux, C., Sifakis, J.: Property preserving simulations. In: CAV. LNCS, vol. 663, pp. 260–273. Springer, Cham (1992). https://doi.org/10.1007/3-540-56496-9_21

  20. Bloom, B., Paige, R.: Transformational design and implementation of a new efficient solution to the ready simulation problem. Sci. Comput. Program. 24(3), 189–220 (1995). https://doi.org/10.1016/0167-6423(95)00003-B

  21. Bouajjani, A., Fernandez, J., Halbwachs, N.: Minimal model generation. In: Clarke, E.M., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 197–203. Springer, Heidelberg (1991). https://doi.org/10.1007/BFb0023733

  22. Brinksma, E., Cleaveland, R., Larsen, K.G., Margaria, T., Steffen, B. (eds.): Tools and Algorithms for Construction and Analysis of Systems, First International Workshop, TACAS ’95, Aarhus, Denmark, 19–20 May 1995, Proceedings, LNCS, vol. 1019. Springer, Cham (1995). https://doi.org/10.1007/3-540-60630-0

  23. Bunte, O., et al.: The mCRL2 toolset for analysing concurrent systems - improvements in expressivity and usability. In: TACAS. LNCS, vol. 11428, pp. 21–39. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17465-1_2

  24. Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on infinite structures. In: Handbook of Process Algebra, pp. 545–623. North-Holland/Elsevier (2001). https://doi.org/10.1016/b978-044482830-9/50027-8

  25. Bustan, D., Grumberg, O.: Simulation based minimization. In: CADE. LNCS, vol. 1831, pp. 255–270. Springer, Cham (2000). https://doi.org/10.1007/10721959_20

  26. Calzolai, F., Nicola, R.D., Loreti, M., Tiezzi, F.: TAPAs: a tool for the analysis of process algebras. Trans. Petri Nets Other Model. Concurr. 1, 54–70 (2008). https://doi.org/10.1007/978-3-540-89287-8_4

  27. Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: CONCUR. LNCS, vol. 3653, pp. 66–80. Springer, Cham (2005). https://doi.org/10.1007/11539452_9

  28. Cerans, K.: Decidability of bisimulation equivalences for parallel timer processes. In: CAV. LNCS, vol. 663, pp. 302–315. Springer, Cham (1992). https://doi.org/10.1007/3-540-56496-9_24

  29. Cerans, K., Godskesen, J.C., Larsen, K.G.: Timed modal specification - theory and tools. In: CAV. LNCS, vol. 697, pp. 253–267. Springer, Cham (1993). https://doi.org/10.1007/3-540-56922-7_21

  30. Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Program. Lang. Syst. 16(5), 1512–1542 (1994). https://doi.org/10.1145/186025.186051

  31. Cleaveland, R., Parrow, J., Steffen, B.: The concurrency workbench. In: Automatic Verification Methods for Finite State Systems. LNCS, vol. 407, pp. 24–37. Springer, Cham (1989). https://doi.org/10.1007/3-540-52148-8_3

  32. Cleaveland, R., Parrow, J., Steffen, B.: The concurrency workbench: a semantics-based tool for the verification of concurrent systems. ACM Trans. Program. Lang. Syst. 15(1), 36–72 (1993). https://doi.org/10.1145/151646.151648

  33. Cleaveland, R., Sims, S.: The NCSU concurrency workbench. In: CAV. LNCS, vol. 1102, pp. 394–397. Springer, Cham (1996). https://doi.org/10.1007/3-540-61474-5_87

  34. Clemente, L.: Büchi automata can have smaller quotients. In: ICALP. LNCS, vol. 6756, pp. 258–270. Springer, Cham (2011). https://doi.org/10.1007/978-3-642-22012-8_20

  35. Clemente, L., Mayr, R.: Efficient reduction of nondeterministic automata with application to language inclusion testing. Log. Methods Comput. Sci. 15(1) (2019). https://doi.org/10.23638/LMCS-15(1:12)2019

  36. Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Trans. Program. Lang. Syst. 19(2), 253–291 (1997). https://doi.org/10.1145/244795.244800

  37. Dams, D., Grumberg, O.: Abstraction and abstraction refinement. In: Handbook of Model Checking, pp. 385–419. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8_13

  38. David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: ECDAR: an environment for compositional design and analysis of real time systems. In: ATVA. LNCS, vol. 6252, pp. 365–370. Springer, Cham (2010). https://doi.org/10.1007/978-3-642-15643-4_29

  39. Dill, D.L., Hu, A.J., Wong-Toi, H.: Checking for language inclusion using simulation preorders. In: CAV. LNCS, vol. 575, pp. 255–265. Springer, Cham (1991). https://doi.org/10.1007/3-540-55179-4_25

  40. Enevoldsen, S., Larsen, K.G., Mariegaard, A., Srba, J.: Dependency graphs with applications to verification. Int. J. Softw. Tools Technol. Transf. 22(5), 635–654 (2020). https://doi.org/10.1007/s10009-020-00578-9

  41. Etessami, K.: A hierarchy of polynomial-time computable simulations for automata. In: CONCUR. LNCS, vol. 2421, pp. 131–144. Springer, Cham (2002). https://doi.org/10.1007/3-540-45694-5_10

  42. Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: CONCUR. LNCS, vol. 1877, pp. 153–167. Springer, Cham (2000). https://doi.org/10.1007/3-540-44618-4_13

  43. Etessami, K., Wilke, T., Schuller, R.A.: Fair simulation relations, parity games, and state space reduction for Büchi automata. SIAM J. Comput. 34(5), 1159–1175 (2005). https://doi.org/10.1137/S0097539703420675

  44. Garavel, H., Lang, F., Mateescu, R., Serwe, W.: CADP 2011: a toolbox for the construction and analysis of distributed processes. Int. J. Softw. Tools Technol. Transf. 15(2), 89–107 (2013). https://doi.org/10.1007/s10009-012-0244-z

  45. Gauwin, O., Muscholl, A., Raskin, M.: Minimization of visibly pushdown automata is NP-complete. Log. Methods Comput. Sci. 16(1) (2020). https://doi.org/10.23638/LMCS-16(1:14)2020

  46. Gentilini, R., Piazza, C., Policriti, A.: From bisimulation to simulation: Coarsest partition problems. J. Autom. Reason. 31(1), 73–103 (2003). https://doi.org/10.1023/A:1027328830731

  47. Gibson-Robinson, T., Armstrong, P.J., Boulgakov, A., Roscoe, A.W.: FDR3 - A modern refinement checker for CSP. In: TACAS. LNCS, vol. 8413, pp. 187–201. Springer, Cham (2014). https://doi.org/10.1007/978-3-642-54862-8_13

  48. Girard, A., Julius, A.A., Pappas, G.J.: Approximate simulation relations for hybrid systems. Discret. Event Dyn. Syst. 18(2), 163–179 (2008). https://doi.org/10.1007/s10626-007-0029-9

  49. Girard, A., Pappas, G.J.: Approximation metrics for discrete and continuous systems. IEEE Trans. Autom. Control. 52(5), 782–798 (2007). https://doi.org/10.1109/TAC.2007.895849

  50. Grumberg, O., Long, D.E.: Model checking and modular verification. ACM Trans. Program. Lang. Syst. 16(3), 843–871 (1994). https://doi.org/10.1145/177492.177725

  51. Gurumurthy, S., Bloem, R., Somenzi, F.: Fair simulation minimization. In: CAV. LNCS, vol. 2404, pp. 610–624. Springer, Cham (2002). https://doi.org/10.1007/3-540-45657-0_51

  52. Heizmann, M., Schilling, C., Tischner, D.: Minimization of visibly pushdown automata using partial Max-SAT. In: TACAS. LNCS, vol. 10205, pp. 461–478 (2017). https://doi.org/10.1007/978-3-662-54577-5_27

  53. Henzinger, T.A.: Hybrid automata with finite bisimulations. In: ICALP. LNCS, vol. 944, pp. 324–335. Springer, Cham (1995). https://doi.org/10.1007/3-540-60084-1_85

  54. Henzinger, T.A.: The theory of hybrid automata. In: LICS. pp. 278–292. IEEE Computer Society (1996). https://doi.org/10.1109/LICS.1996.561342

  55. Henzinger, T.A., Ho, P.: HYTECH: the Cornell HYbrid TECHnology tool. In: Hybrid Systems. LNCS, vol. 999, pp. 265–293. Springer, Cham (1994). https://doi.org/10.1007/3-540-60472-3_14

  56. Henzinger, T.A., Ho, P., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Trans. Autom. Control. 43(4), 540–554 (1998). https://doi.org/10.1109/9.664156

  57. Henzinger, T.A., Kopke, P.W.: State equivalences for rectangular hybrid automata. In: CONCUR. LNCS, vol. 1119, pp. 530–545. Springer, Cham (1996). https://doi.org/10.1007/3-540-61604-7_74

  58. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998). https://doi.org/10.1006/jcss.1998.1581

  59. Henzinger, T.A., Kupferman, O., Rajamani, S.K.: Fair simulation. Inf. Comput. 173(1), 64–81 (2002). https://doi.org/10.1006/inco.2001.3085

  60. Henzinger, T.A., Qadeer, S., Rajamani, S.K., Tasiran, S.: An assume-guarantee rule for checking simulation. ACM Trans. Program. Lang. Syst. 24(1), 51–64 (2002). https://doi.org/10.1145/509705.509707

  61. Henzinger, T.A., Rajamani, S.K.: Fair bisimulation. In: TACAS. LNCS, vol. 1785, pp. 299–314. Springer, Cham (2000). https://doi.org/10.1007/3-540-46419-0_21

  62. Hojati, R.: A BDD-Based Environment for Formal Verification of Hardware Systems. Ph.D. thesis, EECS Department, University of California, Berkeley (1996). https://www2.eecs.berkeley.edu/Pubs/TechRpts/1996/3052.html

  63. Hopcroft, J.E.: An n log n algorithm for minimizing states in a finite automaton. In: Theory of Machines and Computations, pp. 189–196. Academic Press (1971). https://doi.org/10.1016/B978-0-12-417750-5.50022-1

  64. Jančar, P., Srba, J.: Undecidability of bisimilarity by defender’s forcing. J. ACM 55(1), 1–26 (2008). https://doi.org/10.1145/1326554.1326559

  65. Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22(6), 1117–1141 (1993). https://doi.org/10.1137/0222067

  66. Julius, A.A., D’Innocenzo, A., Benedetto, M.D.D., Pappas, G.J.: Approximate equivalence and synchronization of metric transition systems. Syst. Control. Lett. 58(2), 94–101 (2009). https://doi.org/10.1016/j.sysconle.2008.09.001

  67. Juvekar, S., Piterman, N.: Minimizing generalized Büchi automata. In: CAV. LNCS, vol. 4144, pp. 45–58. Springer, Cham (2006). https://doi.org/10.1007/11817963_7

  68. Kucera, A., Mayr, R.: Why is simulation harder than bisimulation? In: CONCUR. LNCS, vol. 2421, pp. 594–610. Springer, Cham (2002). https://doi.org/10.1007/3-540-45694-5_39

  69. Kupferman, O., Vardi, M.Y.: Verification of fair transition systems. Chic. J. Theor. Comput. Sci. 1998 (1998). https://cjtcs.cs.uchicago.edu/articles/1998/2/contents.html

  70. Kučera, A., Jančar, P.: Equivalence-checking with infinite-state systems: Techniques and results. In: SOFSEM. LNCS, vol. 2540, pp. 41–73. Springer, Cham (2002). https://doi.org/10.1007/3-540-36137-5_3

  71. Lanotte, R., Tini, S.: Taylor approximation for hybrid systems. Inf. Comput. 205(11), 1575–1607 (2007), https://doi.org/10.1016/j.ic.2007.05.004

  72. Laroussinie, F., Larsen, K.G., Weise, C.: From timed automata to logic - and back. In: MFCS. LNCS, vol. 969, pp. 529–539. Springer, Cham (1995). https://doi.org/10.1007/3-540-60246-1_158

  73. Larsen, K.G., Nyman, U., Wasowski, A.: On modal refinement and consistency. In: CONCUR. LNCS, vol. 4703, pp. 105–119. Springer, Cham (2007). https://doi.org/10.1007/978-3-540-74407-8_8

  74. Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transf. 1(1–2), 134–152 (1997). https://doi.org/10.1007/s100090050010

  75. Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS, pp. 203–210. IEEE Computer Society (1988). https://doi.org/10.1109/LICS.1988.5119

  76. Larsen, K.G., Yi, W.: Time abstracted bisimulation: Implicit specifications and decidability. In: MFPS. LNCS, vol. 802, pp. 160–176. Springer, Cham (1993). https://doi.org/10.1007/3-540-58027-1_8

  77. Lee, D., Yannakakis, M.: Online minimization of transition systems (extended abstract). In: STOC, pp. 264–274. ACM (1992). https://doi.org/10.1145/129712.129738

  78. Lynch, N.A., Tuttle, M.R.: Hierarchical correctness proofs for distributed algorithms. In: PODC, pp. 137–151. ACM (1987). https://doi.org/10.1145/41840.41852

  79. Majumdar, R., Zamani, M.: Approximately bisimilar symbolic models for digital control systems. In: CAV. LNCS, vol. 7358, pp. 362–377. Springer, Cham (2012). https://doi.org/10.1007/978-3-642-31424-7_28

  80. Mayr, R.: Process rewrite systems. Inf. Comput. 156(1–2), 264–286 (2000). https://doi.org/10.1006/inco.1999.2826

  81. Mayr, R., Clemente, L.: Advanced automata minimization. In: POPL, pp. 63–74. ACM (2013). https://doi.org/10.1145/2429069.2429079

  82. Mazala, R.: Infinite games. In: Automata, Logics, and Infinite Games: a Guide to Current Research. LNCS, vol. 2500, pp. 23–42. Springer, Cham (2001). https://doi.org/10.1007/3-540-36387-4_2

  83. Milner, R.: An algebraic definition of simulation between programs. In: IJCAI, pp. 481–489 (1971). https://ijcai.org/Proceedings/71/Papers/044.pdf

  84. Moller, F.: Infinite results. In: CONCUR. LNCS, vol. 1119, pp. 195–216. Springer, Cham (1996). https://doi.org/10.1007/3-540-61604-7_56

  85. Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987). https://doi.org/10.1137/0216062

  86. Park, D.M.R.: Concurrency and automata on infinite sequences. In: Theoretical Computer Science. LNCS, vol. 104, pp. 167–183. Springer, Cham (1981). https://doi.org/10.1007/BFb0017309

  87. Pola, G., Girard, A., Tabuada, P.: Approximately bisimilar symbolic models for nonlinear control systems. Autom. 44(10), 2508–2516 (2008). https://doi.org/10.1016/j.automatica.2008.02.021

  88. Rauch Henzinger, M., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: FOCS, pp. 453–462. IEEE Computer Society (1995). https://doi.org/10.1109/SFCS.1995.492576

  89. Schewe, S.: Beyond hyper-minimisation–minimising DBAs and DPAs is NP-complete. In: FSTTCS. LIPIcs, vol. 8, pp. 400–411. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010). https://doi.org/10.4230/LIPIcs.FSTTCS.2010.400

  90. Somenzi, F., Bloem, R.: Efficient Büchi automata from LTL formulae. In: CAV. LNCS, vol. 1855, pp. 248–263. Springer, Cham (2000). https://doi.org/10.1007/10722167_21

  91. Srba, J.: Roadmap of infinite results. In: Current Trends in Theoretical Computer Science: The Challenge of the New Century, vol. 2, pp. 337–350. World Scientific (2004)

    Google Scholar 

  92. Srba, J.: Beyond language equivalence on visibly pushdown automata. Log. Methods Comput. Sci. 5(1) (2009). https://arxiv.org/abs/0901.2068

  93. Stirling, C.: Local model checking games. In: CONCUR. LNCS, vol. 962, pp. 1–11. Springer, Cham (1995). https://doi.org/10.1007/3-540-60218-6_1

  94. Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: STOC, pp. 1–9. ACM (1973). https://doi.org/10.1145/800125.804029

  95. Thomas, W.: On the Ehrenfeucht-Fraïssé game in theoretical computer science. In: TAPSOFT. LNCS, vol. 668, pp. 559–568. Springer, Cham (1993). https://doi.org/10.1007/3-540-56610-4_89

  96. Tiwari, A.: Abstractions for hybrid systems. Formal Methods Syst. Des. 32(1), 57–83 (2008). https://doi.org/10.1007/s10703-007-0044-3

  97. Urabe, N., Hasuo, I.: Fair simulation for nondeterministic and probabilistic Büchi automata: a coalgebraic perspective. Log. Methods Comput. Sci. 13(3) (2017). https://doi.org/10.23638/LMCS-13(3:20)2017

  98. Yi, W.: CCS + time = an interleaving model for real time systems. In: ICALP. LNCS, vol. 510, pp. 217–228. Springer, Cham (1991). https://doi.org/10.1007/3-540-54233-7_136

Download references

Acknowledgments

This research was partly supported by DIREC - Digital Research Centre Denmark and the Villum Investigator Grant S4OS.

Author information

Authors and Affiliations

  1. Department of Computer Science, Aalborg University, Aalborg, Denmark

    Kim G. Larsen, Christian Schilling & Jiří Srba

Authors
  1. Kim G. Larsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Schilling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiří Srba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Schilling .

Editor information

Editors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Jean-François Raskin

  2. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Krishnendu Chatterjee

  3. École Normale Supérieure Paris-Saclay, Gif-sur-Yvette, France

    Laurent Doyen

  4. MPI for Software Systems, Kaiserslautern, Germany

    Rupak Majumdar

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Larsen, K.G., Schilling, C., Srba, J. (2022). Simulation Relations and Applications in Formal Methods. In: Raskin, JF., Chatterjee, K., Doyen, L., Majumdar, R. (eds) Principles of Systems Design. Lecture Notes in Computer Science, vol 13660. Springer, Cham. https://doi.org/10.1007/978-3-031-22337-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-22337-2_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22336-5

  • Online ISBN: 978-3-031-22337-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics