| Autor: |
Mardare, Radu, Panangaden, Prakash, Plotkin, Gordon |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
36th Anual Symposium on Logics in Computer Science, ACM/IEEE LICS 2021 |
| Druh dokumentu: |
Working Paper |
| Popis: |
We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of approximate equality rather than exact equality. The result is a novel theory of fixed points which can not only provide solutions to the traditional fixed-point equations but we can also define the rate of convergence to the fixed point. We show that such a theory is the quantitative analogue of a Conway theory and also of an iteration theory; and it reflects the metric coinduction principle. We study the Bellman equation for a Markov decision process as an illustrative example. |
| Databáze: |
arXiv |
| Externí odkaz: |
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