reducer.lua

--[[
MIT License

Copyright (c) 2019 emmachase

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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]]

local dr = {}

local pprint = require("pprint")
local util = require("util")

local function isEpsilon(condition)
  return type(condition) == "table" and condition.type == "epsilon"
end

local function traverseEpsilon(machine, state, seen)
  seen = seen or {}

  local func = {state}

  local edges = machine.states[state].edges
  for i = 1, #edges do
    local edge = edges[i]
    if isEpsilon(edge.condition) then
      if not seen[edge.dest] then
        seen[edge.dest] = true

        -- Epsilon transition, add to E function
        func[#func + 1] = edge.dest

        -- Traverse through its destination and fully evaluate the epsilon path
        local extraFn = traverseEpsilon(machine, edge.dest, seen)

        -- Append those new states to this E function
        local pos = #func
        for j = 1, #extraFn do
          func[pos + 1] = extraFn[j]
          pos = pos + 1
        end
      end
    end
  end

  return util.nub(func)
end

local function nameFromST(st)
  table.sort(st)
  return table.concat(st)
end

function dr.reduceNFA(nfa)
  -- Construct E function
  local eFunc = {}
  for k in pairs(nfa.states) do
    local eI = 1
    eFunc[k] = traverseEpsilon(nfa, k)
  end

  local newMachine = {
    states = {},
    startState = nameFromST(eFunc[nfa.startState]),
    acceptStates = {},
    properties = nfa.properties
  }

  local todoStates = {eFunc[nfa.startState]}
  local completeStates = {}

  while todoStates[1] do -- while todoStates is not empty
    local workingState = table.remove(todoStates, 1)
    local newState = {
      edges = {},
      enter = {}
    }

    local lang = {}

    local isAccepted = false

    -- Get all possible inputs by traversing states
    for i = 1, #workingState do
      local stateName = workingState[i]
      if nfa.acceptStates[stateName] then
        isAccepted = true
      end

      local state = nfa.states[stateName]
      for j = 1, #state.edges do
        local cond = state.edges[j].condition
        if type(cond) == "string" then
          lang[cond] = lang[cond] or {}
          lang[cond][#lang[cond] + 1] = state.edges[j].dest
        end
      end
    end

    -- For each possible input, compute the resultant state, and create an edge
    for k, v in pairs(lang) do
      local st, si = {}, 1

      for i = 1, #v do
        local throughput = eFunc[v[i]]
        for j = 1, #throughput do
          st[si] = throughput[j]
          si = si + 1
        end
      end

      st = util.nub(st)
      table.sort(st)

      local destState = nameFromST(st)
      newState.edges[#newState.edges + 1] = {
        condition = k,
        dest = destState
      }

      if not completeStates[destState] then
        todoStates[#todoStates + 1] = st
        completeStates[destState] = true
      end
    end

    -- Append each enter condition
    local ei = 1
    for i = 1, #workingState do
      local stateName = workingState[i]
      local state = nfa.states[stateName]

      if state.enter then
        for j = 1, #state.enter do
          newState.enter[ei] = state.enter[j]
          ei = ei + 1
        end
      end
    end

    local stateName = nameFromST(workingState)
    newMachine.states[stateName] = newState
    if isAccepted then
      newMachine.acceptStates[stateName] = true
    end

    completeStates[stateName] = true
  end

  return newMachine
end

return dr