# Sesqui-Pushout Rewriting: Concurrency, Associativity and Rule Algebra Framework

## TL;DR

This paper introduces a concurrency theorem and associativity property for sesqui-pushout (SqPO) graph rewriting, enabling the development of rule algebras and stochastic models for complex transformations.

## Contribution

It provides the first concurrency theorem and associativity framework for SqPO rewriting, facilitating algebraic and probabilistic analysis of graph transformations.

## Key findings

- Established a concurrency theorem for SqPO rewriting
- Proved associativity property for SqPO rule compositions
- Constructed rule algebras for stochastic rewriting systems

## Abstract

Sesqui-pushout (SqPO) rewriting is a variant of transformations of graph-like and other types of structures that fit into the framework of adhesive categories where deletion in unknown context may be implemented. We provide the first account of a concurrency theorem for this important type of rewriting, and we demonstrate the additional mathematical property of a form of associativity for these theories. Associativity may then be exploited to construct so-called rule algebras (of SqPO type), based upon which in particular a universal framework of continuous-time Markov chains for stochastic SqPO rewriting systems may be realized.