Add text-based parser for easier pushdown automaton creation

[Copilot]

This PR implements a text-based parser that allows users to create pushdown automata using mathematical notation instead of manually constructing objects. This addresses the need for a more "text-parsy" approach to defining PDAs.

Problem

Previously, creating a pushdown automaton required verbose manual construction:

const automaton = new PushdownAutomaton();
const startState = new State("q0");
const endState = new State("q1");
const transition = new TransitionFunction("a", endState, "$", ["X", "$"]);
startState.addTransitionFunction(transition);
automaton.setStartSate(startState);
automaton.addEndState(endState);

Solution

Now users can define PDAs using standard mathematical notation:

const definition = `
  States: q0, q1, q2
  Start State: q0
  Final States: q2
  Initial Stack Symbol: $
  
  # Language: a^n b^n (n >= 1)
  δ(q0, a, $) = (q0, Z$)
  δ(q0, a, Z) = (q0, ZZ)
  δ(q0, b, Z) = (q1, ε)
  δ(q1, b, Z) = (q1, ε)
  δ(q1, ε, $) = (q2, $)
`;

const automaton = PushdownAutomaton.fromDefinition(definition);

Features Added

• Mathematical notation parser: Supports standard PDA transition notation δ(state, input, stack) = (next_state, stack_push)
• Simple configuration API: Alternative object-based configuration for programmatic use
• Static factory methods: PushdownAutomaton.fromDefinition() and PushdownAutomaton.fromSimpleConfig()
• Epsilon transition support: Handles ε, epsilon, and empty string notations
• Comment support: Lines starting with # are ignored
• Flexible notation: Supports both δ and delta function names

Enhanced Automaton Engine

The parser required improvements to the core automaton to properly handle epsilon transitions:

• Enhanced epsilon transition processing for empty input strings
• Added stack empty state handling to prevent runtime errors
• Improved transition ordering for correct stack semantics
• Maintains full backward compatibility with existing API

Examples

Balanced Parentheses:

const definition = `
  States: q0, q1
  Start State: q0
  Final States: q1
  Initial Stack Symbol: $
  
  δ(q0, ε, $) = (q1, $)
  δ(q0, (, $) = (q0, X$)
  δ(q0, (, X) = (q0, XX)
  δ(q0, ), X) = (q0, ε)
  δ(q1, (, $) = (q0, X$)
`;

Context-Free Language a^n b^n:

const definition = `
  States: q0, q1, q2
  Start State: q0
  Final States: q2
  Initial Stack Symbol: $
  
  δ(q0, a, $) = (q0, Z$)
  δ(q0, a, Z) = (q0, ZZ)
  δ(q0, b, Z) = (q1, ε)
  δ(q1, b, Z) = (q1, ε)
  δ(q1, ε, $) = (q2, $)
`;

Testing

• 66 tests with 100% pass rate
• 94.81% statement coverage, 87.01% branch coverage
• Comprehensive unit tests for parser functionality
• Integration tests with real-world PDA examples (balanced parentheses, context-free languages, palindromes)
• All existing functionality remains unchanged and tested

This enhancement makes the library significantly more accessible while maintaining the full power and flexibility of the underlying automaton engine.

---

💬 Share your feedback on Copilot coding agent for the chance to win a $200 gift card! Click here to start the survey.