Abstract
We provide a relation-algebraic characterization of liveness in Petri nets based on a relation-algebraic definition of both the structure and the state space of Petri nets. Such an approach, compared to the common ones that apply predicate logic and set theory, shifts the formalization to a more abstract level. As a main benefit, Petri net properties can be proved in a rigorous mathematical style. Since the characterizations are executable relational specifications, they provide the possibility for tool support.
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Berghammer, R., Fronk, A.: Applying relational algebra in 3D graphical software design. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2003. LNCS, vol. 3051, pp. 62–73. Springer, Heidelberg (2004)
Berghammer, R., Karger, B., Ulke, C.: Relational-algebraic analysis of Petri nets with RelView. In: Margaria, T., Steffen, B. (eds.) TACAS 1996. LNCS, vol. 1055, pp. 49–69. Springer, Heidelberg (1996)
Berghammer, R., Zierer, H.: Relational algebraic semantics of deterministic and nondeterministic programs. Theoretical Computer Science 43, 123–147 (1996)
Doberkat, E.-E.: Pipelines: Modelling a software architecture through relations. Acta Informatica 40, 37–79 (2003)
Finkel, A.: The minimal coverability graph for Petri nets. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 210–243. Springer, Heidelberg (1993)
Fronk, A.: Using relation algebra for the analysis of Petri nets in a CASE tool based approach. In: 2nd IEEE International Conference on Software Engineering and Formal Methods (SEFM), Beijing, pp. 396–405. IEEE, Los Alamitos (2004)
Fronk, A., Kehden, B.: State space analysis of petri nets with relation-algebraic methods. Journal of Symbolic Computation 44, 15–47 (2009)
Fronk, A., Pleumann, J.: Relation-algebraic Analysis of Petri Nets: Concepts and Implementation. Petri Net News Letters, 61–68 (April 2005)
Fronk, A., Pleumann, J.: On Relational Cycles. In: MacCaull, W., Winter, M., Düntsch, I. (eds.) RelMiCS 2005. LNCS, vol. 3929, pp. 83–95. Springer, Heidelberg (2006)
Leoniuk, B.: ROBDD-based implementation of relational algebra with applications. Dissertation, Universität Kiel (2001) (in German)
Milanese, U.: On the implementation of a ROBDD-based tool for the manipulation and visualization of relations. Dissertation, Universität Kiel (2003) (in German)
Pastor, E., Roig, O., Cortadella, J., Badia, R.M.: Petri net analysis using Boolean manipulation. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 416–435. Springer, Heidelberg (1994)
Reisig, W.: Petri nets: an introduction. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1985)
Schmidt, G., Ströhlein, T.: Relations and graphs. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)
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Fronk, A., Berghammer, R. (2009). A Relation-Algebraic Approach to Liveness of Place/Transition Nets. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_8
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DOI: https://doi.org/10.1007/978-3-642-04639-1_8
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