2021-03-04: Radu Mardare (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Radu Mardare (MSP)

Quantitative Iteration Theories

Abstract

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.

This is a recent joint work with Gordon Plotkin and Prakash Panangaden.

2021-03-04 15:00:00 UTC
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