Context-free languages via coalgebraic trace semantics (2005)
| Venue: | International Conference on Algebra and Coalgebra in Computer Science (CALCO’05), volume 3629 of Lect. Notes Comp. Sci |
| Citations: | 11 - 8 self |
BibTeX
@INPROCEEDINGS{Hasuo05context-freelanguages,
author = {Ichiro Hasuo and Bart Jacobs},
title = {Context-free languages via coalgebraic trace semantics},
booktitle = {International Conference on Algebra and Coalgebra in Computer Science (CALCO’05), volume 3629 of Lect. Notes Comp. Sci},
year = {2005},
pages = {213--231},
publisher = {Springer}
}
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Abstract
Abstract. We show that, for functors with suitable mild restrictions, the initial algebra in the category of sets and functions gives rise to the final coalgebra in the (Kleisli) category of sets and relations. The finality principle thus obtained leads to the finite trace semantics of nondeterministic systems, which extends the trace semantics for coalgebras previously introduced by the second author. We demonstrate the use of our technical result by giving the first coalgebraic account on contextfree grammars, where we obtain generated context-free languages via the finite trace semantics. Additionally, the constructions of both finite and possibly infinite parse trees are shown to be monads. Hence our extension of the application domain of coalgebras identifies several new mathematical constructions and structures. 1
