DeepAI AI Chat
Log In Sign Up

Separator logic and star-free expressions for graphs

07/29/2021
by   Mikołaj Bojańczyk, et al.
0

We describe two formalisms for defining graph languages, and prove that they are equivalent: 1. Separator logic. This is first-order logic on graphs which is allowed to use the edge relation, and for every n ∈{0,1,…} a relation of arity n+2 which says that "vertex s can be connected to vertex t by a path that avoids vertices v_1,…,v_n". 2. Star-free graph expressions. These are expressions that describe graphs with distinguished vertices called ports, and which are built from finite languages via Boolean combinations and the operations on graphs with ports used to construct tree decompositions. Furthermore, we prove a variant of Schützenberger's theorem (about star-free languages being those recognized by a periodic monoids) for graphs of bounded pathwidth. A corollary is that, given k and a graph language represented by an formula, one can decide if the language can be defined in either of two equivalent formalisms on graphs of pathwidth at most k.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/23/2022

On star-multi-interval pairwise compatibility graphs

A graph G is a star-k-PCG if there exists a non-negative edge weighted s...
01/30/2023

Cops and robbers on P_5-free graphs

We prove that every connected P_5-free graph has cop number at most two,...
09/01/2020

Reconfiguration graphs of zero forcing sets

This paper begins the study of reconfiguration of zero forcing sets, and...
01/04/2019

Star sampling with and without replacement

Star sampling (SS) is a random sampling procedure on a graph wherein eac...
07/13/2018

Characterising AT-free Graphs with BFS

An asteroidal triple free graph is a graph such that for every independe...
06/26/2019

A Stricter Heap Separating Points-To Logic

Dynamic memory issues are hard to locate and may cost much of a developm...
04/03/2021

From n-grams to trees in Lindenmayer systems

In this paper we present two approaches to Lindenmayer systems: the rule...