Epsilon logic-gate transitions, closure

Epsilon-logic-gate (ε-logic-gate) Implementation

Non-deterministic Finite Automata with Epsilon Transitions

What is an Epsilon-logic-gate (ε-logic-gate)?

An Epsilon-logic-gate (ε-logic-gate) is a Non-deterministic Finite Automaton that allows epsilon (ε) transitions - transitions that can be taken without consuming any input symbol. This makes ε-NFAs even more flexible than regular NFAs for representing regular languages.

An ε-logic-gate is formally defined as a 5-tuple (Q, Σ, δ, q₀, F) where:

  • Q: Finite set of states
  • Σ: Finite set of input symbols (alphabet)
  • δ: Transition function δ: Q × (Σ ∪ {ε}) → P(Q)
  • q₀: Initial state (q₀ ∈ Q)
  • F: Set of final/accepting states (F ⊆ Q)
Key Concept - Epsilon Closure (ε-closure): The ε-closure of a state q is the set of all states reachable from q using only ε-transitions (including q itself).

Example ε-logic-gate

ε-logic-gate that accepts strings ending with "01" over alphabet {0, 1}

q₀
ε
q₁
0
q₂
1
q₃
States: q₀ (start), q₁, q₂, q₃ (final)
Transition Table
State Input 0 Input 1 ε
q₀ {q₀} {q₀} {q₁}
q₁ {q₂} ∅ ∅
q₂ ∅ {q₃} ∅
q₃ ∅ ∅ ∅

Custom ε-logic-gate Builder

Build your own ε-logic-gate with epsilon transitions and test strings

ε-logic-gate Configuration
Transition Function (including ε-transitions)

Enhanced ε-logic-gate simulator

Test strings with detailed epsilon closure visualization

1x
Mode:
0ms Avg Time
0 ε-Closures
O(1) Complexity

ε-logic-gate Statistics

States: 4
Transitions: 5
ε-Transitions: 1
Alphabet Size: 2
Tests Run: 0
Acceptance Rate: 0%
Quick Test Strings
ε-Closure Calculator

Visual ε-logic-gate Diagram

Batch Testing with ε-Closure Analysis

Test multiple strings and analyze epsilon closure behavior

ε-logic-gate to logic-gate Conversion

See how the current ε-logic-gate can be converted to an equivalent logic-gate