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2011

Quantitative Kleene coalgebras

9 years 5 months ago
Quantitative Kleene coalgebras
We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA’s) and Milner (on regular behaviours and finite LTS’s), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new...
Alexandra Silva, Filippo Bonchi, Marcello M. Bonsa
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where IANDC
Authors Alexandra Silva, Filippo Bonchi, Marcello M. Bonsangue, Jan J. M. M. Rutten
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