Por Melissa Antonelli (University of Helsinki).

Implicit computational complexity is an active area of theoretical computer science, aiming to provide machine-independent characterizations of relevant complexity classes. One of the seminal works in this field appeared in 1964, when Cobham introduced a function algebra closed under bounded recursion on notation and able to capture FP, the class of functions computable in polynomial time. Since then, several complexity classes have been characterized using limited recursion schemas. Recently, an elegant algebra was defined by Bournez and Durand, who, in 2019, showed that ordinary differential equations (ODEs) offer a natural tool for algorithmic design and characterized FP via a special ODE schema. The overall goal of our study is precisely that of generalizing this approach to parallel computation and of providing (possibly uniform) ODE-style characterizations for small circuit classes. In particular, in this talk I will present the global aim and methodology at the basis of our in progress study and sketch our first result, namely our proposal for an original characterization of AC0 due to ODEs.

[Joint work with A. Durand and J. Kontinen]

Transmissão via Zoom.