DFAs

Deterministic Finite Automata are NFAs with two additional constraints: no epsilon transitions, and exactly one transition per state per symbol. Use dfa() from delta:lib.

Basic Structure

import { dfa } from 'delta:lib'
 
const machine = dfa('name')
  .alphabet(...)
  .states(...)
  .start(...)
  .accept(...)
  .transition(...)
  .build()

DFABuilder extends NFABuilder, so all NFA methods are available — including .bounce(), .plus(), .increment(), .batch(), .all(), and state scoping via .state().

Additional Constraints

No Epsilon Transitions

Calling .transition(from, EPS, to) on a DFA builder is an error.

Total Transition Function

Every declared state must have exactly one outgoing transition for every symbol in the alphabet. Missing or duplicate transitions are both errors — .build() will throw if either condition is violated.

// If q1 is a dead state, it still needs all transitions defined
.transition('q1', 'a', 'q1')
.transition('q1', 'b', 'q1')

.increment(...symbols)

This helper is particularly useful for DFAs that count modular sequences. It wires all declared states into a circular chain — each state advances to the next on the given symbol, and the last state wraps back to the first:

import { dfa, q } from 'delta:lib'
 
dfa('mod-3')
  .states(...q(0, 2)) // q0, q1, q2
  .increment('a')     // q0→q1→q2→q0

Validation

.build() throws NFABuildError if there are any errors. In a DFA, missing transitions that would be warnings in an NFA are promoted to errors.