# Seminar of Manlio Valenti

## A formal definition of complexity

# Manlio Valenti

# Date: 23/03/2017 at 12.00pm

# Where: Aula Seminari, Dipartimento di Matematica

*Abstract*: While the notion of complexity is somewhat intuitive, it is not trivial to define it formally. A possible solution is the one suggested by Kolmogorov, who exploited the framework of computability theory to define a function that ``measures the complexityā€¯ of a string. This function, despite the fact that it is incomputable, matches the intuitive idea of complexity in many ways. The notion of Kolmogorov complexity marks the beginning of the branch of mathematics called Algorithmic Information Theory. We will also discuss the relation between Kolmogorov complexity and probability theory and how we can address the problem of sequence prediction in this context.