Speaker: Matteo Mio – CNRS, ENS-Lyon

Title: An introduction to Quantitative Algebras

Abstract:

Equational reasoning and equational manipulations are widespread in all areas of computer science. Consider, for example, the optimisation steps performed by a compiler which replaces blocks of code with “equivalent”, but more efficient, blocks. In recent years it has become apparent that sometimes “approximate” equational reasoning techniques are useful and/or necessary. A block of code might be replaced by another block which is not truly equivalent but, say, equivalent 99% of the time (in a certain statistical sense). In this talk I will present the basic ideas of the mathematical framework of “Quantitative Algebras”, recently proposed by Mardare et. al. in [1], aiming at formally developing some of the intuitions mentioned above.

[1] Radu Mardare, Prakash Panangaden, and Gordon Plotkin. 2016. Quantitative Algebraic Reasoning. In Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2016). Association for Computing Machinery, New York, NY, USA, 700–709. https://doi.org/10.1145/2933575.2934518