Language acceptance by Deterministic Finite Automata (DFAs)

Getting Started

The simulation interface consists of three main components:

  1. DFA State Diagram: A visual representation of the current automaton showing states and transitions
  2. Input String Panel: Displays the current input string being processed
  3. Execution Trace: Shows the step-by-step execution history

Available DFA Examples

The simulation includes five pre-configured DFA examples:

  1. DFA 1: Accepts strings that begin with "01"
  2. DFA 2: Accepts strings containing exactly three 1s
  3. DFA 3: Accepts strings that end with "0"
  4. DFA 4: Accepts strings with at least one 0 and ending with 1
  5. DFA 5: Accepts strings where the first occurrence of 0 is in a group of at least three consecutive 0s

Step-by-Step Instructions

1. Selecting a DFA

Click the "Change DFA" button to cycle through the five available automata. Each DFA has a description explaining the language it accepts. The current DFA's description is displayed above the state diagram.

2. Choosing Input Strings

Click the "Change Input" button to cycle through different pre-configured test strings for the current DFA. Each DFA comes with multiple example strings that demonstrate both accepted and rejected cases.

3. Understanding the Interface

  • Start State: Marked with an incoming arrow and typically labeled "A"
  • Accept States: Shown with double circles
  • Current State: Highlighted in blue during execution
  • Processed Characters: Displayed with a darker background in the input string
  • Current Character: Highlighted with a distinct color

4. Stepping Through Execution

Initial Setup

When you load a DFA and input string, the automaton starts in the initial state before processing any characters.

Forward Execution

Click the "Next Step" button to advance the automaton one character at a time:

  • The current character is highlighted in the input string
  • The automaton transitions to the next state according to the transition function
  • Each step is recorded in the execution trace
  • The current state is visually highlighted in the diagram

Backward Execution

Click the "Previous" button to step backward through the execution:

  • Returns to the previous state
  • Removes the last step from the execution trace
  • Updates the input string highlighting

5. Interactive Guessing Feature

The simulation includes an interactive quiz mode that helps reinforce learning:

How It Works

  • When clicking "Next Step", you may be prompted to guess the next state
  • A modal dialog appears showing the current state and character being read
  • Select your predicted next state from the available options
  • Receive immediate feedback on your guess

Streak System

  • Correct guesses increase your current streak
  • Your best streak is automatically saved
  • Incorrect guesses reset your current streak
  • Use the "Reset" button to clear your streak counters

Skip Option

If you're unsure about a transition, you can click "Skip Guess" to proceed without making a prediction, though this will reset your current streak.

6. Reading the Execution Trace

The execution trace panel provides a detailed history of the automaton's execution:

  • Each line shows a state transition
  • Format: "State X --character--> State Y"
  • Special notation for string completion and acceptance/rejection
  • Automatically scrolls to show the most recent steps

7. Understanding Results

String Acceptance

  • If the automaton ends in an accept state after processing all characters, the string is accepted
  • The final trace entry will indicate "String Accepted"

String Rejection

  • If the automaton ends in a non-accept state after processing all characters, the string is rejected
  • The final trace entry will indicate "String Rejected"