Abstract
Process algebras with data, such as LOTOS, PSF, FDR, and mCRL2, are very suitable to model and analyse combinatorial problems. Contrary to more traditional mathematics, many of these problems can very directly be formulated in process algebra. Using a wide range of techniques, such as behavioural reductions, model checking, and visualisation, the problems can subsequently be easily solved. With the advent of probabilistic process algebras this also extends to problems where probabilities play a role. In this paper we model and analyse a number of very well-known – yet tricky – problems and show the elegance of behavioural analysis.
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Notes
- 1.
The tools are by Olav Bunte (evaluation of modal formulas on probabilistic transition systems) and Ferry Timmers (probabilistic trace reduction).
References
Hadley, J., Singmaster, D.: Problems to sharpen the young. Math. Gaz. 76(475), 102–126 (1992). doi:10.2307/3620384
Bekič, H.: Towards a mathematical theory of processes. Technical report TR25.125, IBM Laboratory, Vienna (1971). Also appeared in Jones, C.B. (ed.) Programming Languages and Their Definition, Lecture Notes in Computer Science, vol. 177. Springer (1984)
Bergstra, J.A., Klop, J.W.: Fixed point semantics in process algebras. Report IW 206, Mathematisch Centrum, Amsterdam (1982)
Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Inf. Comput. 60(1/3), 109–137 (1984)
Biemans, F., Blonk, P.: On the formal specification and verification of CIM architectures using LOTOS. Comput. Ind. 7(6), 491–504 (1986)
Blackburn, P., van Benthem, J., Wolter, F. (eds.): Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3. Elsevier, Amsterdam (2007)
Brinksma, E., Karjoth, G.: A specification of the OSI transport service in LOTOS. In: Yemini, Y., Strom, R.E., Yemini, S. (eds.) Protocol Specification, Testing and Verification IV, pp. 227–251. North-Holland, Amsterdam (1984)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). doi:10.1007/BFb0025774
van Ditmarsch, H., van der Hoek, W., Kooij, B.: Dynamic Epistemic Logic. Studies in Epistemology, Logic, Methodology, and Philosophy of Science, vol. 337. Springer, Heidelberg (2008). doi:10.1007/978-1-4020-5839-4
Dijkstra, E.W.: Pruning the search tree. EWD1255. www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EWD1255.html. Accessed June 2017
van Emde Boas, P., Groenendijk, J., Stokhof, M.: The conway paradox: its solution in an epistemic framework. In: Groenendijk, J., Janssen, T.M.V., Stokhof, M. (eds.) Truth, Interpretation, and Information: Selected Papers from the Third Amsterdam Colloquium, pp. 159–182. Foris Publications, New York (1984)
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)
Gardner, M.: My Best Mathematical and Logic Puzzles. Dover, Downers Grove (1994)
Gibson-Robinson, T., Armstrong, P., Boulgakov, A., Roscoe, A.W.: FDR3 — a modern refinement checker for CSP. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 187–201. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54862-8_13
Cranen, S., Groote, J.F., Reniers, M.A.: A linear translation from CTL* to the first-order modal \(\mu \)-calculus. Theoret. Comput. Sci. 412(28), 3129–3139 (2011)
Groote, J.F., van Ham, F.: Interactive visualization of large state spaces. Int. J. Softw. Tools Technol. Transf. 8(1), 77–91 (2006)
Groote, J.F., Mousavi, M.R.: Modeling and Analysis of Communication Systems. The MIT Press, Cambridge (2014). (See for the toolset www.mcrl2.org)
Groote, J.F., Ponse, A.: The syntax and semantics of \(\mu \)CRL. Report CS-R9076, CWI, Amsterdam (1990)
Grünwald, P., Halpern, J.Y.: Updating probabilities. In: Darwiche, A., Friedman, N. (eds.) Uncertainty in Artificial Intelligence, pp. 187–196. Morgan Kaufman, Burlington (2002)
Hennessy, M., Milner, R.: On observing nondeterminism and concurrency. In: de Bakker, J., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 299–309. Springer, Heidelberg (1980). doi:10.1007/3-540-10003-2_79
Hoare, C.A.R.: Communicating sequential processes. Commun. ACM 21(8), 666–677 (1978)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall International, Upper Saddle River (1985)
Kozen, D.: Results on the propositional \(\mu \)-calculus. Theoret. Comput. Sci. 27, 333–354 (1983)
ISO 8807:1989. Information processing systems - Open Systems Interconnection - LOTOS - A formal description technique based on the temporal ordering of observational behaviour. ISO/IECJTC1/SC7 (1989)
Milner, R.: An approach to the semantics of parallel programs. In: Proceedings Convegno di Informatica Teorica, pp. 283–302, Pisa (1973)
Mauw, S., Veltink, G.J.: A process specification formalism. Fundam. Inform. XIII, 85–139 (1990)
Milner, R.: Processes: a mathematical model of computing agents. In: Rose, H.E., Shepherdson, J.C. (eds.) Proceedings Logic Colloquium 1972, pp. 158–173. North-Holland, Amsterdam (1973)
Milner, R. (ed.): A Calculus of Communicating Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Pnueli, A.: The temporal logic of programs. In: Foundations of Computer Science, pp. 46–57. IEEE, Piscataway (1977)
Prior, A.N.: Time and Modality. Oxford University Press, Oxford (1957)
Roscoe, A.W.: Understanding Concurrent Systems. Springer, Heidelberg (2010). doi:10.1007/978-1-84882-258-0
van Sinderen, M., Ajubi, I., Caneschi, F.: The application of LOTOS for the formal description of the ISO session layer. In: Turner, K.J. (ed.) Formal Description Techniques, pp. 263–277. North-Holland, Amsterdam (1989)
Winkler, P.: Mathematical Puzzles. A Connaisseur’s Collection. A.K. Peters, Natick (2004)
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The authors are grateful to the reviewers for their constructive and inspiring comments.
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Groote, J.F., de Vink, E.P. (2017). Problem Solving Using Process Algebra Considered Insightful. In: Katoen, JP., Langerak, R., Rensink, A. (eds) ModelEd, TestEd, TrustEd. Lecture Notes in Computer Science(), vol 10500. Springer, Cham. https://doi.org/10.1007/978-3-319-68270-9_3
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