Abstract
Causal trees are one of the earliest pioneering contributions of Pierpaolo Degano, in joint work with Philippe Darondeau. The idea is to record causality dependencies in processes and in their actions. As such, causal trees sit between interleaving models and truly concurrent ones and they originate an abstract, event-based bisimulation semantics for causal processes, where, intuitively, minimal causal trees represent the semantic domain. In the paper we substantiate this feeling, by first defining a nominal, compositional operational semantics based on History-Dependent automata and then we apply categorical techniques, based on named-sets, showing that causal trees form the final coalgebra semantics of a suitable coalgebraic representation of causal behaviour.
Research supported by MIUR PRIN Project CINA Prot. 2010LHT4KM and by NWO Project 612.001.113 Practical Coinduction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
An analogous concept of location automata was introduced in [14] for modelling the location semantics of CCS.
- 2.
As it is common in final semantics, the final coalgebra is typically an infinite object that accounts for all possible behaviours, but the minimal representative of an HD-automaton needs to account just for the behaviours of that automaton: it decomposes uniquely the map from the HD-automaton to the final object into a surjective mapping from the HD-automaton to the representative and an embedding of the latter into the final object.
- 3.
Note that inactive agents of the form \(K \mathbin {\vdash }\mathbf {0}\) are just disregarded.
References
Basagni, S.: A note on causal trees and their applications to CCS. Int. J. Comput. Math. 71(2), 137–159 (1999)
Bodei, C.: Some concurrency models in a categorical framework. In: ICTCS (1998)
Bruni, R., Montanari, U., Sammartino, M.: A coalgebraic semantics for causality in Petri nets. J. Logic Algebr. Meth. Progr. (2015, in press). http://cs.ru.nl/M.Sammartino/publications/JLAMP15.pdf
Bruni, R., Montanari, U., Sammartino, M.: Revisiting causality, coalgebraically. Acta Inf. 52(1), 5–33 (2015). http://www.cs.ru.nl/M.Sammartino/publications/ACTA2014.pdf
Ciancia, V., Kurz, A., Montanari, U.: Families of symmetries as efficient models of resource binding. Electr. Notes Theor. Comput. Sci. 264(2), 63–81 (2010)
Ciancia, V., Montanari, U.: Symmetries, local names and dynamic (de)-allocation of names. Inf. Comput. 208(12), 1349–1367 (2010)
Darondeau, P., Degano, P.: Causal trees. In: Dezani-Ciancaglini, M., Ronchi Della Rocca, S., Ausiello, G. (eds.) ICALP 1989. LNCS, vol. 372, pp. 234–248. Springer, Heidelberg (1989)
Darondeau, P., Degano, P.: Causal trees interleaving + causality. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 239–255. Springer, Heidelberg (1990)
Fiore, M.P., Turi, D.: Semantics of name and value passing. In: LICS, pp. 93–104 (2001)
Fröschle, S.B., Hildebrandt, T.T.: On plain and hereditary history-preserving bisimulation. In: Kutyłowski, M., Wierzbicki, T.M., Pacholski, L. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 354–365. Springer, Heidelberg (1999)
Fröschle, S.B., Lasota, S.: Causality versus true-concurrency. Theor. Comput. Sci. 386(3), 169–187 (2007)
Gadducci, F., Miculan, M., Montanari, U.: About permutation algebras, (pre)sheaves and named sets. Higher-Order Symbolic Comput. 19(2–3), 283–304 (2006)
Montanari, U., Pistore, M.: Minimal transition systems for history-preserving bisimulation. In: Morvan, M., Reischuk, R. (eds.) STACS 1997. LNCS, vol. 1200, pp. 413–425. Springer, Heidelberg (1997)
Montanari, U., Pistore, M., Yankelevich, D.: Efficient minimization up to location equivalence. In: Riis Nielson, H. (ed.) ESOP 1996. LNCS, vol. 1058, pp. 265–279. Springer, Heidelberg (1996)
Pistore, M.: History dependent automata. Ph.D. thesis, University of Pisa (1999)
Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bruni, R., Montanari, U., Sammartino, M. (2015). Causal Trees, Finally. In: Bodei, C., Ferrari, G., Priami, C. (eds) Programming Languages with Applications to Biology and Security. Lecture Notes in Computer Science(), vol 9465. Springer, Cham. https://doi.org/10.1007/978-3-319-25527-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-25527-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25526-2
Online ISBN: 978-3-319-25527-9
eBook Packages: Computer ScienceComputer Science (R0)