# Tracelets and Tracelet Analysis Of Compositional Rewriting Systems

## TL;DR

This paper introduces tracelets, a novel minimal derivation trace concept that leverages associativity in rule compositions to enhance the analysis of rewriting systems, enabling static generation of minimal traces with specific outcomes.

## Contribution

It extends classical concurrency theory by defining tracelets, providing a new framework for trace abstraction and analysis in rewriting systems.

## Key findings

- Tracelets are minimal, compositional derivation traces.
- The framework captures causality and equivalence classes of derivations.
- A prototype algorithm for static minimal trace generation is presented.

## Abstract

Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for rewriting systems over adhesive categories. We introduce the notion of tracelets, which are defined as minimal derivation traces that universally encode sequential compositions of rewriting rules. Tracelets are compositional, capture the causality of equivalence classes of traditional derivation traces, and intrinsically suggest a clean mathematical framework for the definition of various notions of abstractions of traces. We illustrate these features by introducing a first prototype for a framework of tracelet analysis, which as a key application permits to formulate a first-of-its-kind algorithm for the static generation of minimal derivation traces with prescribed terminal events.