### November 8, 2021

**Théo Grente**(LACL)

Conjunctive grammars are an extension of context free grammars with a conjunction operation. Their expressive power (even on a unary alphabet) is largely unknown.

When restricting time, space or even communication, cellular automata (CA) can act as languages recognizer defining complexity classes.

The goal of this talk is to prove the inclusion of conjunctive languages in one of CA complexity classes.

The proof uses a programming method which relies on exact characterizations of interesting CA complexity classes by sub-logics of ESO (existential second-order logic) with Horn formulas as their first-order part. By using this method, we just have to define conjunctive grammars in our logic to obtain an inclusion result.