# On the Comparison of Context-Free Grammars

## TL;DR

This paper presents a method for comparing context-free grammars by reducing the problem to solving nonlinear matrix equations, laying the groundwork for automated, probabilistic assessment tools in computer science education.

## Contribution

It introduces a novel approach that connects grammar comparison to numerical solutions of matrix equations, enabling probabilistic and automated analysis.

## Key findings

- Reduction of grammar comparison to matrix equations
- Foundation for probabilistic comparison algorithms
- Potential application in automated student answer assessment

## Abstract

In this paper we consider the problem of context-free grammars comparison from the analysis point of view. We show that the problem can be reduced to numerical solution of systems of nonlinear matrix equations. The approach presented here forms a basis for probabilistic comparison algorithms oriented to automatic assessment of of student's answers in computer science.