Defining Context-Free Power Series Coalgebraically
In this paper we present a coinductive definition of context free power series in terms of behavioural differential equations. We show that our coalgebraic approach provides a unified view on many, at first sight different, existing notions of algebraicity, and we apply our behavioural differential equations to produce a new proof for a classical result by Chomsky and Schützenberger, and a simple proof that the zip-operator of two algebraic streams is algebraic.
- [AS03]Allouche, J.-P., Shallit, J.O.: Automatic Sequences – Theory, Applications, Generalizations. Cambridge University Press (2003)Google Scholar
- [BR11]Berstel, J., Reutenauer, C.: Noncommutative Rational Series with Applications. Cambridge University Press (2011)Google Scholar
- [PS09]Petre, I., Salomaa, A.: Algebraic systems and pushdown automata. In: Handbook of Weighted Automata, 1st edn., pp. 257–289. Springer (2009)Google Scholar
- [SBBR10]Silva, A., Bonchi, F., Bonsangue, M., Rutten, J.: Generalizing the powerset construction, coalgebraically. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2010. LIPIcs, vol. 8, pp. 272–283 (2010)Google Scholar