Abstract
In this paper a way to have structures with partiality in its internal structure in a categorical approach is presented and, with this, a category of partial graphs \(\mathcal{G}r_{p}\) is given and partial automata are constructed from \(\mathcal{G}r_{p}\). With a simple categorical operation, computations of partial automata are given and can be seen as a part of the structure of partial automata.
This work is partially supported by CAPES, CNPq and FAPERGS.
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
Preview
Unable to display preview. Download preview PDF.
References
Peterson, J.L.: Petri Net Theory and the Modelling of Systems. Prentice-Hall, New Jersey (1981)
Meseguer, J., Montanari, U.: Petri nets are monoids. Information and Computation 88, 105–155 (1990)
Menezes, P.B.: Diagonal compositionality of partial petri nets. In: 2nd US-Brazil Joint Workshops on the Formal Foundations of Software Systems. Eletronic Notes in Theoretical Computer Science, vol. 14 (1998)
Hopcroft, J.E.: Introduction to automata theory, languages and computation. Addison-Wesley, Reading (1979)
Adamek, J., Trnkova, V.: Automata and Algebras in Categories, 1st edn. Kluwer, Dordrecht (1990)
Hoff, M.A., Roggia, K.G., Menezes, P.B.: Composition of Transformations: A Framework for Systems with Dynamic Topology. International Journal of Computing Anticipatory Systems 14, 259–270 (2004)
Bénabou, J.: Introduction to bicategories. In: Reports of the Midwest Category Seminar. Springer Lecture Notes in Mathematics, vol. 47, pp. 1–77. Springer, Heidelberg (1967)
Borceux, F.: Handbook of Categorical Algebra 1: Basic Category Theory. Encyclopedia of Mathematics and Its Applications, vol. 50. Cambridge University Press, Cambridge (1994)
Asperti, A., Longo, G.: Categories, Types, and Structures - An Introduction to Category Theory for the Working Computer Scientist. MIT Press, Cambridge (1991)
Rutten, J.J.M.M.: Automata and coinduction (an exercise in coalgebra). In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 194–218. Springer, Heidelberg (1998)
Bruni, R., Gadducci, F.: Some algebraic laws for spans. In: Kahl, W., Parnas, D., Schmidt, G. (eds.) Proceedings of RelMiS 2001, Workshop on Relational Methods in Software. Electronic Notes in Theoretical Computer Science, vol. 3(44). Elsevier Science, Amsterdam (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Roggia, K.G., Hoff, M.A., Menezes, P.B. (2005). Computation of Partial Automata Through Span Composition. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_3
Download citation
DOI: https://doi.org/10.1007/11556985_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29002-5
Online ISBN: 978-3-540-31829-3
eBook Packages: Computer ScienceComputer Science (R0)