Abstract
This paper discusses issues that arise when process algebras and Petri nets are linked; in particular, operators, compositional ity, recursion, refinement and equivalences. It uses the box algebra in order to show how Petri nets can be manipulated algebraically. Also, the paper shows how other process algebras such as CCS, COSY and CSP can be treated in the same way, how Petri net semantics of concurrent programming languages can be given, and how Petri net methods can be applied to the verification of concurrent algorithms.
This work has been done in cooperation with other people, in particular Javier Esparza, Jon G. Hall and Richard P Hopkins. It has been supported by the Esprit Basic Research Project 3148 DEMON (Design Methods Based on Nets) and Working Group 6067 CALIBAN (Causal Calculi Based on Nets).
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References
J. Baeten, WP Weijland: Process Algebra. Cambridge Tracts in Theoretical Computer Science 18 (1990).
E. Best: Representing a Program Invariant as a Linear Invariant in a Petri Net. Bulletin of the European Association of Theoretical Computer Science Vol. 17, 2–11 (1982).
E. Best: Semantics of Sequential and Parallel Programs. Prentice Hall (1996).
E. Best: Partial Order Verification with PEP Proc. POMIV'96, Partial Order Methods in Verification, G. Holzmann, D. Peled, V. Pratt (eds). American Mathematical Society, Series in Discrete Mathematics and Theoretical Computer Science Vol. 29, 305–328 (1996).
E. Best, R. Devillers: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science Vol. 55/1, 87–136 (1988).
E. Best, R. Devillers, J. Esparza: General Refinement and Recursion Operators for the Petri Box Calculus. Springer-Verlag, Lecture Notes in Computer Science Vol. 665, 130–140 (1993).
E. Best, R. Devillers, J.G. Hall: The Petri Box Calculus: a New Causal Algebra with Multilabel Communication. Advances in Petri Nets 1992, G.Rozenberg (ed.), Springer-Verlag, Lecture Notes in Computer Science Vol. 609, 21–69 (1992).
E. Best, R. Devillers, M. Koutny: Petri Net Algebra (Working Title). Manuscript (1997).
E. Best, H. Fleischhack, W. Frączak, R.P. Hopkins, H. Klaudel, E. Pelz: An M-net Semantics of B(PN) 2. Proc. STRICT'95, Berlin, J. Desel (ed.). Springer-Verlag, Workshops in Computing, 85–100 (1995).
E. Best, M. Koutny: Solving Recursive Net Equations. Proc. ICALP-95, Springer-Verlag, Lecture Notes in Computer Science Vol.944, 605–623 (1995).
G.Boudol, I.Castellani: Flow Models of Distributed Computations: Event Structures and Nets. Rapport de Recherche, INRIA, Sophia Antipolis (July 1991).
G. Bruns, J. Esparza: Trapping Mutual Exclusion in the Box Calculus. Theoretical Computer Science Vol. 153/1-2, 95–128 (1995).
P. Degano, R. De Nicola, U. Montanari: A Distributed Operational Semantics for CCS Based on C/E Systems. Acta Informatica Vol. 26, 59–91 (1988).
J. Desel, J. Esparza: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science 40, Cambrige University Press (1995).
R. Devillers: Construction of S-invariants and S-components for Refined Petri Boxes. Proceedings of Petri Nets'93, Chicago, LNCS 691, Springer-Verlag (1993).
R. Devillers: S-invariant Analysis of Recursive Petri Boxes. Acta Informatica Vol. 32, 313–345 (1995).
Cited in: E.W. Dijkstra: Cooperating Sequential Processes. Programming Languages, F. Genuys (ed.), 43–112. Academic Press (1968).
E.W. Dijkstra: A Discipline of Programming. Prentice Hall (1976).
J. Esparza: Model Checking based on Branching Processes. Habilitation, Hildesheim (1993). Published as: Model Checking Using Net Unfoldings. Proc. TAPSOFT'93 (1993), M.C. Gaudel, J.P Jouannaud (eds). Springer-Verlag, LNCS Vol. 668, 613–628 (1993). Full version in Science of Computer Programming Vol. 23, 151–195 (1994).
H.J. Genrich, K. Lautenbach, PS. Thiagarajan: Elements of General Net Theory. Net Theory and Applications, Proc. of the Advanced Course on General Net Theory of Processes and Systems, W. Brauer (ed.). Lecture Notes in Computer Science Vol. 84, Springer-Verlag, 21–163 (1980).
U. Goltz: On Representing CCS Programs by Finite Petri Nets. Proc. MFCS'88, Springer-Verlag, Lecture Notes in Computer Science Vol. 324, 339–350 (1988).
U. Goltz, R. Loogen: A Non-interleaving Semantic Model for Nondeterministic Concurrent Processes. Fundamenta Informaticae Vol. 14/1, 39–73 (1991).
U. Goltz, W. Reisig: The Non-sequential Behaviour of Petri Nets. Information and Control Vol. 57/2-3, 125–147 (1983).
J. Grabowski: On Partial Languages. Fundamenta Informaticae Vol. IV/2, 427–498 (1981).
C.A.R. Hoare: Communicating Sequential Processes. Prentice Hall (1985).
R. Janicki, PE. Lauer: Specification and Analysis of Concurrent Systems — the COSY Approach. Springer-Verlag, EATCS Monographs on Theoretical Computer Science (1992).
K. Jensen: Coloured Petri Nets. Basic Concepts. EATCS Monographs on Theoretical Computer Science, Springer-Verlag (1992).
M. Koutny, and E. Best: Operational Semantics for the Box Algebra. Hildesheimer Informatikbericht Nr.33/95 (October 1995). To appear in Theoretical Computer Science (1998).
A. Mazurkiewicz: Trace Theory. In: Petri Nets: Applications and Relationships to Other Models of Concurrency, Advances in Petri Nets 1986, Part II, W. Brauer, W. Reisig, G. Rozenberg (eds.), Springer-Verlag, Lecture Notes in Computer Science Vol. 255, 279–324 (1987).
K.L. McMillan: Using Unfoldings to Avoid the State Explosion Problem in the Verification of Asynchronous Circuits. Proc. 4th Workshop on Computer Aided verification, 164–174 (1992).
R. Milner: A Calculus of Communicating Systems. Springer-Verlag, Lecture Notes in Computer Science Vol. 92 (1980).
R. Milner: Communication and Concurrency. Prentice Hall (1989).
J.H. Morris: A Starvation-free Solution to the Mutual Exclusion Problem. Information Processing Letters Vol. 8/2, 76–80 (1979).
T. Murata: Petri Nets: Properties, Analysis and Applications. Proc. IEEE Vol. 77/4, 541–580 (1989).
E.-R. Olderog: Nets, Terms and Formulas. Cambridge Tracts in Theoretical Computer Science 23 (1991).
S.S. Owicki, D. Gries: An Axiomatic Proof Technique for Parallel Programs. Acta Informatica Vol. 6, 319–340 (1976).
PEP. the home page of PEP (a Programming Environment Based of Petri Nets) is http://www.informatik.uni-hildesheim.de/ pep/HomePage.html.
G.L. Peterson: Myths about the Mutual Exclusion Problem. Information Processing Letters Vol. 12/3, 115–116 (1981).
G. Plotkin: A Structural Approach to Operational Semantics. DAIMI Technical Report FN-19, Computer Science Department, University of Århus (1981).
W. Reisig: Petri Nets. An Introduction. EATCS Monographs on Theoretical Computer Science Vol. 3, Springer-Verlag (1985).
W. Reisig: Modelling and Verification of Distributed Algorithms. Proc. CONCUR'96, U. Montanari, V. Sassone (eds), Springer-Verlag, LNCS Vol. 1119, 579–595 (1996).
P.H. Starke: Processes in Petri Nets. Elektronische Informationsverarbeitung und Kybernetik Vol. 17/8-9, 389–416 (1981).
D. Taubner: Finite Representation of CCS and TCSP Programs by Automata and Petri Nets. Springer-Verlag, Lecture Notes in Computer Science Vol. 369 (1989).
B. Teßmer: S-und T-Invarianten zum Nachweis von Eigenschaften paralleler Algorithmen. Diplomarbeit (Januar 1996).
W. Vogler: Partial Words versus Processes: a Short Comparison. Advances in Petri Nets 1992, G.Rozenberg (ed.). Springer-Verlag, Lecture Notes in Computer Science Vol. 609, 292–303 (1992).
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Best, E., Devillers, R., Koutny, M. (1998). Petri nets, process algebras and concurrent programming languages. In: Reisig, W., Rozenberg, G. (eds) Lectures on Petri Nets II: Applications. ACPN 1996. Lecture Notes in Computer Science, vol 1492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-65307-4_46
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