Quantitative Kleene coalgebras

@article{Silva2011QuantitativeKC,
  title={Quantitative Kleene coalgebras},
  author={Alexandra Silva and Filippo Bonchi and Marcello M. Bonsangue and Jan J. M. M. Rutten},
  journal={Inf. Comput.},
  year={2011},
  volume={209},
  pages={822-849}
}
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… CONTINUE READING
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