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Finite-State Automaton To/From Regular Expression Visualization

Marco T. Morazán, Tijana Minić

TL;DR

The paper tackles the educational challenge of intuitively teaching the bidirectional transformations between nondeterministic finite automata and regular expressions. It introduces FSM, a domain-specific language in Racket, alongside graph-based GNFA-driven visualizations that support forward and backward stepping through regexp-to-ndfa and ndfa-to-regexp transformations, with automatic GNFA construction to reduce user burden. Key contributions include per-step, explanatory visualizations rendered via Graphviz, an interface that lowers extraneous cognitive load, and empirical data from a control group indicating high usefulness and ease of use across novices. The work has practical impact for FLAT classrooms and lays groundwork for extending these visualizations to broader language-derivation tasks and parse-tree representations.

Abstract

Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these transformations are rarely intuitive. To assist students with such transformations, visualization tools can play a pivotal role. This article presents visualization tools developed for FSM -- a domain-specific language for the Automata Theory classroom -- to transform a finite state automaton to a regular expression and vice versa. Using these tools, the user may provide an arbitrary finite-state machine or an arbitrary regular expression and step forward and step backwards through a transformation. At each step, the visualization describes the step taken. The tools are outlined, their implementation is described, and they are compared with related work. In addition, empirical data collected from a control group is presented. The empirical data suggests that the tools are well-received, effective, and learning how to use them has a low extraneous cognitive load.

Finite-State Automaton To/From Regular Expression Visualization

TL;DR

The paper tackles the educational challenge of intuitively teaching the bidirectional transformations between nondeterministic finite automata and regular expressions. It introduces FSM, a domain-specific language in Racket, alongside graph-based GNFA-driven visualizations that support forward and backward stepping through regexp-to-ndfa and ndfa-to-regexp transformations, with automatic GNFA construction to reduce user burden. Key contributions include per-step, explanatory visualizations rendered via Graphviz, an interface that lowers extraneous cognitive load, and empirical data from a control group indicating high usefulness and ease of use across novices. The work has practical impact for FLAT classrooms and lays groundwork for extending these visualizations to broader language-derivation tasks and parse-tree representations.

Abstract

Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these transformations are rarely intuitive. To assist students with such transformations, visualization tools can play a pivotal role. This article presents visualization tools developed for FSM -- a domain-specific language for the Automata Theory classroom -- to transform a finite state automaton to a regular expression and vice versa. Using these tools, the user may provide an arbitrary finite-state machine or an arbitrary regular expression and step forward and step backwards through a transformation. At each step, the visualization describes the step taken. The tools are outlined, their implementation is described, and they are compared with related work. In addition, empirical data collected from a control group is presented. The empirical data suggests that the tools are well-received, effective, and learning how to use them has a low extraneous cognitive load.
Paper Structure (19 sections, 1 equation, 11 figures)

This paper contains 19 sections, 1 equation, 11 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Construction Algorithms
  4. regexp to ndfa
  5. ndfa to regexp
  6. Visualization
  7. regexp to ndfa Visualization
  8. ndfa to regexp
  9. A Brief Introduction to FSM
  10. Regular Expressions
  11. Finite-State Automatons
  12. Overall Visualization Design
  13. Illustrative Example: regexp to ndfa
  14. Illustrative Example: ndfa to regexp
  15. Implementation
  16. ...and 4 more sections

Figures (11)

  • Figure 1: Initial step in the JFLAP visualization.
  • Figure 2: Resulting transition diagrams for L={$ab^{\texttt{*}} \cup ba^{\texttt{*}}$}.
  • Figure 3: An ndfa for the language L={w $|$ w is missing at least one in {a b c}}.
  • Figure 4: JFLAP visualization states.
  • Figure 5: JFLAP's and FSM's final visualization state.
  • ...and 6 more figures