// eNFA that does not accept any string
def eNFA_ZERO(): NFA[TState, Char] = {
  val Q = TState()
  NFA(Set(Q), { case _ => Set() }, Set())
}

// eNFA that accepts the empty string
def eNFA_ONE() : NFA[TState, Char] = {
  val Q = TState()
  NFA(Set(Q), { case _ => Set() }, Set(Q))
}

// eNFA that accepts the string "c"
def eNFA_CHAR(c: Char) : NFA[TState, Char] = {
  val Q1 = TState()
  val Q2 = TState()
  NFA(Set(Q1), { case (Q1, d) if (c == d) => Set(Q2) }, Set(Q2))
}

// alternative of two eNFAs
def eNFA_ALT(enfa1: NFA[TState, Char], enfa2: NFA[TState, Char]) : NFA[TState, Char] = {
  val Q = TState()
  val new_delta : eNFAtrans = 
    { case (Q, None) => enfa1.starts | enfa2.starts }

  val new_fins = (q: TState) => enfa1.fins(q) || enfa2.fins(q)

  eNFA(Set(Q), 
       new_delta andAlso enfa1.delta andAlso enfa2.delta, 
       new_fins)
}

// sequence of two eNFAs
def eNFA_SEQ(enfa1: NFA[TState, Char], enfa2: NFA[TState, Char]) : NFA[TState, Char] = {
  val new_delta : eNFAtrans = 
    { case (q, None) if enfa1.fins(q) => enfa2.starts }
  
  eNFA(enfa1.starts, 
       new_delta andAlso enfa1.delta andAlso enfa2.delta, 
       enfa2.fins)
}

// star of an eNFA
def eNFA_STAR(enfa: NFA[TState, Char]) : NFA[TState, Char] = {
  val Q = TState()
  val new_delta : eNFAtrans = 
    { case (Q, None) => enfa.starts
      case (q, None) if enfa.fins(q) => Set(Q) }

  eNFA(Set(Q), new_delta andAlso enfa.delta, Set(Q))
}