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The compositional constructionof Markov processes II

Published online by Cambridge University Press:  15 March 2011

L. de Francesco Albasini ,
N. Sabadini  and
R. F.C. Walters
L. de Francesco Albasini
Affiliation:
Dipartimento di Fisica e Matematica, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy; [email protected]
N. Sabadini
Affiliation:
Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Carloni 78, 22100 Como, Italy; {nicoletta.sabadini};{robert.walters}@uninsubria.it
R. F.C. Walters
Affiliation:
Dipartimento di Informatica e Comunicazione, Università degli Studi dell'Insubria, via Carloni 78, 22100 Como, Italy; {nicoletta.sabadini};{robert.walters}@uninsubria.it
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Abstract

We add sequential operations to the categorical algebra of weighted andMarkov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, 
arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones withevolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].

Keywords

Categorical algebraMarkov processweighted automatonhierarchicaldistributed
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 45 , Issue 1: ICTCS 09 , January 2011 , pp. 117 - 142
Copyright
© EDP Sciences, 2011

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References

C. Baier, M. Grösser and F. Ciesinski, Model checking linear-time properties of probabilistic systems. Handbook of Weighted Automata. EATCS Monographs in Theoretical Computer Science (2009), 519–596.
Blass, A., Seven trees in one. J. Pure Appl. Algebra 103 (1991) 1–21. CrossRef
S.L. Bloom and Z. Ésik, Iteration Theories. EATCS Monographs on Theoretical Computer Science (1993).
R. Blute, A. Edalat and P. Panangaden, Bisimulation for Labelled Markov Processes, Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science (1997), 95–106.
Carboni, A. and Walters, R.F.C., Cartesian bicategories I. J. Pure Appl. Algebra 49 (1987) 11–32. CrossRef
B. Coecke and D. Pavlovic, Quantum measurements without sums, in Mathematics of Quantum Computing and Technology. G. Chen, L. Kauffman and S. Lamonaco, Eds. Chapman & Hall (2007), 567–604.
B. Coecke and S. Perdrix, Environment and classical channels in categorical quantum mechanics. arXiv:1004.1598 (2010).
L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, The parallel composition of processes, ART 2008. Analysing Reduction systems using Transition systems, Forum, Udine (2008), 111–121 (also arXiv:0904.3961).
L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, The compositional construction of Markov processes. arXiv:0901.2434.
L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, Cospans and spans of graphs: a categorical algebra for the sequential and parallel composition of discrete systems. arXiv:0909.4136.
M. Droste, W. Kuich and H. Vogler, Eds., Handbook of Weighted Automata. EATCS Monographs in Theoretical Computer Science (2009).
S. Eilenberg, Automata, Languages, and Machines A. Academic Press, New York (1974).
Harel, D., Statecharts: a visual formalism for complex systems. Sci. Comput. Program. 8 (1987) 231–274. CrossRef
Hasegawa, M., On traced monoidal closed categories. Math. Struct. Comput. Sci. 19 (2009) 217–244. CrossRef
J. Hillston, A Compositional Approach to Performance Modelling. Cambridge University Press (1996).
C.A.R. Hoare, Communicating Sequential Processes. Prentice Hall (1985).
Joyal, A., Street, R. and Verity, D., Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119 (1996) 447–468. CrossRef
P. Katis, N. Sabadini and R.F.C. Walters, Span (Graph): A categorical algebra of transition systems, Proc. AMAST '97, SLNCS, Vol. 1349. Springer Verlag (1997), 307–321.
Katis, P., Sabadini, N. and Walters, R.F.C., A formalisation of the IWIM Model. A. Porto and G.-C. Roman, Eds., in Proc. Coordination 2000. Lecture Notes in Computer Science 1906 (2000) 267–283. CrossRef
J. Kock, Frobenius algebras and 2D topological Quantum Field Theories. Cambridge University Press (2004).
F.W. Lawvere, Some remarks on the future of category theory, Proceedings Category Theory 1990. Lecture Notes in Mathematics 1488 (1991) 1–13.
Lynch, N.A., Segala, R. and Vaandrager, F.W., Observing branching structure through probabilistic contexts. SIAM J. Comput. 37 (2007) 977–1013. CrossRef
R. Milner, A Calculus of Communicating Systems. Springer Verlag (1980).
A. Pnueli and L. Zuck, Probabilistic verification by tableaux, in Proceedings LICS'86. IEEE Computer Society Press (1986), 322–331.
Rabin, M.O., Probabilistic Automata. Inform. Control 6 (1963) 230–245. CrossRef
Rosebrugh, R., Sabadini, N. and Walters, R.F.C., Generic commutative separable algebras and cospans of graphs. Theory and Applications of Categories 15 (2005) 264–177.
R. Segala, Modeling and Verification of Randomized Distributed Real-Time Systems, Ph.D. thesis, MIT Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA (1995). Also, Technical Report MIT/LCS/TR-676.
P. Sobociński, A non-interleaving process calculus for multi-party synchronisation, Procedings ICE '09 (2009).
A. Sokolova and E.P. de Vink, Probabilistic automata: system types, parallel composition and comparison. Lecture Notes in Computer Science 2925 (2004) 1–43.
Gh. Stefanescu, Network Algebra. Springer Verlag (2000).
R.J. van Glabbeek, S.A. Smolka and B. Steffen, Reactive, generative and stratified models of probabilistic processes. Inform. Comput. (1995).
M. Vardi, Automatic verification of probabilistic concurrent finite-state programs, in Proceedings FOCS'85. IEEE Computer Society Press (1985), 327–338.