Algorithm for transforming context-free expressions into equivalent L-graphs

Abstract

This work examines context-free grammars and their alternative representations—context-free expressions and context-free L-graphs. A context-free expression serves as an algebraic form for representing context-free grammars, matching known methods in conciseness while simultaneously providing a more detailed and visual demonstration of how language strings are generated from subordinate strings. A context-free L-graph is a directed graph whose arcs are labeled with symbols from a primary alphabet and additional bracket markers that affect the successful traversal of a path from the initial vertex to the final vertex (bracket balance is required). This article focuses on the algorithm for converting context- free expressions into equivalent L-graphs. The proposed algorithm is accompanied by a correctness proof and incorporates the idea of removing redundant vertices. Such a synthesis of algebraic and graphical approaches combines their key advantages: on one hand, context-free expressions ensure compact and clear descriptions, while on the other hand, context-free L-graphs provide intuitive visualization of the language structure. This combined approach opens prospects for developing more effective tools for analyzing and transforming language models in compilers and text processing systems.