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Finite State Machine Mealy Moore Karnaugh Minimization Tutor

· Last updated：2026-08-17

Step-by-step tutor for automata and combinational logic: ε-NFA/NFA → DFA subset construction, Moore minimization, Mealy↔Moore conversion, Karnaugh maps and exact Quine-McCluskey minimization with tables, ASCII diagrams and every round shown.

Details

What this tool helps you do

Automaton DSL with states/start/accept/alphabet headers and from symbol to transitions; Mealy outputs as q0 a q1 / 1, Moore via moore:. Boolean mode takes minterms and don't-cares for a Gray-coded K-map and QM with essential prime implicants and an exact minimum cover.

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Written by the Elysia Tools team

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Education
Input types
select, textarea, number, text, checkbox
Output type
html
Sample coverage
4
API ready
Yes

Overview

This finite state machine and Boolean minimization tutor provides step-by-step results for ε-NFA and NFA subset construction, DFA minimization, Mealy and Moore conversion, Karnaugh maps, and exact Quine-McCluskey minimization. Enter an automaton definition or Boolean function inputs to receive tables, ASCII diagrams, implicant details, and intermediate calculation rounds.

When to use

  • Convert an ε-NFA or NFA into a DFA with subset construction and ε-closures.
  • Minimize a DFA with Moore partition refinement or convert Mealy and Moore machines when outputs are provided.
  • Minimize a Boolean function using a Gray-coded Karnaugh map and exact Quine-McCluskey coverage.

How it works

  1. 1Select Automata mode or Boolean minimization mode.
  2. 2In Automata mode, enter states, start and accepting states, alphabet symbols, and transitions using the supported definition format.
  3. 3Enable DFA conversion, DFA minimization, or Mealy↔Moore conversion as needed.
  4. 4In Boolean mode, provide the variable count, ON-set minterms, and optional don't-care terms to calculate the minimal SOP.

Use cases

  • Study ε-closures, subset construction, DFA minimization, and state equivalence with every intermediate round visible.
  • Check Mealy and Moore output mappings while learning how output-labeled transitions affect machine states.
  • Verify digital logic reductions by comparing Karnaugh map groups with Quine-McCluskey prime implicants and the exact minimum cover.

Examples

1. Convert and minimize an ε-NFA for (a|b)*abb

Automata student

Background

A student wants to verify the classic 11-state ε-NFA for the regular expression (a|b)*abb and inspect each determinization and minimization stage.

Problem

Construct the DFA and reduce it to a minimum equivalent machine.

How to use

Select Automata mode, enter the states, transitions, start state, accepting state, and alphabet, then enable Convert NFA to DFA and Minimize DFA.

Automaton definition: states 0 through 10; start state 0; accept state 10; alphabet a and b; include the ε-NFA transitions for (a|b)*abb.

Outcome

The tutor shows a verified 5-state DFA with only E accepting, followed by a 4-state minimal DFA and the closure and partition-refinement rounds.

2. Minimize a four-variable Boolean function

Digital logic learner

Background

A learner needs to reduce f = Σm(0,1,2,5,6,7,8,9,10,14) and compare map-based grouping with an exact tabular method.

Problem

Find the minimal sum-of-products expression and identify essential prime implicants.

How to use

FAQ

What automata formats does the tutor accept?

Use headers for states, start, accept, and alphabet, followed by transitions in the form `from symbol to`. Use ε or eps for epsilon transitions.

Can it convert an NFA or ε-NFA to a DFA?

Yes. Enable subset construction to calculate ε-closures and construct the corresponding DFA.

How does DFA minimization work?

The tutor removes unreachable states and applies Moore partition refinement, showing the refinement rounds.

How are Mealy and Moore machines entered?

Enter Mealy outputs as `q0 a q1 / 1`. Define Moore outputs with a `moore:` declaration such as `moore: q0:0 q1:1`.

What Boolean minimization inputs are required?

Select 2 to 4 variables, enter the ON-set minterms, and optionally provide don't-care terms. The tutor returns a Karnaugh grouping and an exact minimal SOP cover.

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Select Boolean minimization, set Number of variables to 4, enter the listed minterms, and leave Don't-cares empty.

Minterms: `0,1,2,5,6,7,8,9,10,14`

Outcome

The result identifies 6 prime implicants, essential implicants B'C' and CD', and the unique minimal SOP B'C' + CD' + A'BD with 3 terms and 7 literals.

3. Inspect a machine with Mealy or Moore outputs

Finite-state machine designer

Background

A learner has a small labeled state machine and wants to study its output representation alongside the transition structure.

Problem

Represent output-labeled transitions or state outputs and apply the available automata analysis.

How to use

Select Automata mode, enter the state and transition definitions, add Mealy outputs with `from symbol to / output` or Moore outputs with a `moore:` declaration, then enable output conversion.

Outcome

The tutor parses the supplied output model and presents the corresponding automata analysis, including the Mealy↔Moore conversion when applicable.