# On Grammars, Polytopes, and Groups

#### Fri, Nov 8, 2019 12:30 CET

######
**Speakers:**
Mateus de Oliveira Oliveira

A fundamental step towards solving combinatorial problems using techniques from linear programming theory is to encode the space of feasible solutions for such problems as the set of vertices of polytopes of small extension complexity.

In this work, we establish several connections between the extension complexity of polytopes, formal language theory, and group theory. In particular, we introduce the notion of homogeneous context-free grammars and show that polytopes corresponding to languages accepted by polynomial-size non-uniform families of grammars with polynomial homogeneity have polynomial extension complexity. Using this result we show that groups that can be embedded into the automorphism group of graphs of constant treewidth and constant degree have polynomial extension complexity.

Joint work with Lars Jaffke and Hans Raj Tiwary.