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package utm.scala
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import scala.annotation.tailrec
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import scala.language.implicitConversions
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/**
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* Implementation of Universal Turing Machine in Scala that can simulate an arbitrary
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* Turing machine on arbitrary input
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*
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* @author Abdulla Abdurakhmanov (https://github.com/abdolence/utms)
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*/
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class UniversalTuringMachine[S](
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val rules: List[UTMRule[S]],
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val initialState: S,
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val finalStates: Set[S],
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val blankSymbol: String,
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val inputTapeVals: Iterable[String],
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printEveryIter: Int = 1
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) {
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private val initialTape = UTMTape( inputTapeVals.toVector, 0, blankSymbol )
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@tailrec
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private def iterate( state: S, curIteration: Int, tape: UTMTape ): UTMTape = {
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if (curIteration % printEveryIter == 0) {
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print( s"${curIteration}: ${state}: " )
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tape.printTape()
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}
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if (finalStates.contains( state )) {
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println( s"Finished in the final state: ${state}" )
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tape.printTape()
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tape
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} else {
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rules.find(rule => rule.state == state && rule.fromSymbol == tape.current() ) match {
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case Some( rule ) => {
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val updatedTape = tape.updated( rule.toSymbol, rule.action )
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iterate( rule.toState, curIteration + 1, updatedTape )
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}
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case _ => {
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println(
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s"Finished: no suitable rules found for ${state}/${tape.current()}"
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)
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tape.printTape()
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tape
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}
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}
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}
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}
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def run(): UTMTape =
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iterate( state = initialState, curIteration = 0, tape = initialTape )
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}
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/**
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* Universal Turing Machine actions
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*/
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sealed trait UTMAction
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object UTMAction {
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case object left extends UTMAction
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case object right extends UTMAction
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case object stay extends UTMAction
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}
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/**
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* Universal Turing Machine rule definition
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*/
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case class UTMRule[S]( state: S, fromSymbol: String, toSymbol: String, action: UTMAction, toState: S )
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object UTMRule {
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implicit def tupleToUTMLRule[S](
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tuple: ( S, String, String, UTMAction, S )
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): UTMRule[S] =
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UTMRule[S]( tuple._1, tuple._2, tuple._3, tuple._4, tuple._5 )
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}
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/**
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* Universal Turing Machine Tape
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*/
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case class UTMTape( content: Vector[String], position: Int, blankSymbol: String ) {
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private def updateContentAtPos( symbol: String ) = {
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if (position >= content.length) {
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content :+ symbol
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} else if (position < 0) {
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symbol +: content
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} else if (content( position ) != symbol)
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content.updated( position, symbol )
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else
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content
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}
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private[scala] def updated( symbol: String, action: UTMAction ): UTMTape = {
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val updatedTape =
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this.copy( content = updateContentAtPos( symbol ), position = action match {
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case UTMAction.left => position - 1
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case UTMAction.right => position + 1
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case UTMAction.stay => position
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} )
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if (updatedTape.position < 0) {
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updatedTape.copy(
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content = blankSymbol +: updatedTape.content,
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position = 0
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)
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} else if (updatedTape.position >= updatedTape.content.length) {
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updatedTape.copy( content = updatedTape.content :+ blankSymbol )
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} else
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updatedTape
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}
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private[scala] def current(): String = {
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if (content.isDefinedAt( position ))
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content( position )
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else
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blankSymbol
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}
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def printTape(): Unit = {
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print( "[" )
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if (position < 0)
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print( "˅" )
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content.zipWithIndex.foreach {
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case ( symbol, index ) =>
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if (position == index)
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print( "˅" )
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else
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print( " " )
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print( s"$symbol" )
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}
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if (position >= content.length)
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print( "˅" )
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println( "]" )
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}
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}
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object UniversalTuringMachine extends App {
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main()
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def main(): Unit = {
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import UTMAction._
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def createIncrementMachine() = {
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sealed trait IncrementStates
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case object q0 extends IncrementStates
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case object qf extends IncrementStates
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new UniversalTuringMachine[IncrementStates](
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rules = List( ( q0, "1", "1", right, q0 ), ( q0, "B", "1", stay, qf ) ),
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initialState = q0,
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finalStates = Set( qf ),
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blankSymbol = "B",
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inputTapeVals = Seq( "1", "1", "1" )
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).run()
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}
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def createThreeStateBusyBeaver() = {
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sealed trait ThreeStateBusyStates
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case object a extends ThreeStateBusyStates
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case object b extends ThreeStateBusyStates
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case object c extends ThreeStateBusyStates
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case object halt extends ThreeStateBusyStates
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new UniversalTuringMachine[ThreeStateBusyStates](
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rules = List(
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( a, "0", "1", right, b ),
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( a, "1", "1", left, c ),
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( b, "0", "1", left, a ),
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( b, "1", "1", right, b ),
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( c, "0", "1", left, b ),
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( c, "1", "1", stay, halt )
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),
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initialState = a,
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finalStates = Set( halt ),
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blankSymbol = "0",
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inputTapeVals = Seq()
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).run()
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}
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def createFiveState2SymBusyBeaverMachine() = {
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sealed trait FiveBeaverStates
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case object FA extends FiveBeaverStates
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case object FB extends FiveBeaverStates
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case object FC extends FiveBeaverStates
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case object FD extends FiveBeaverStates
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case object FE extends FiveBeaverStates
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case object FH extends FiveBeaverStates
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new UniversalTuringMachine[FiveBeaverStates](
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rules = List(
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( FA, "0", "1", right, FB ),
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( FA, "1", "1", left, FC ),
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( FB, "0", "1", right, FC ),
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( FB, "1", "1", right, FB ),
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( FC, "0", "1", right, FD ),
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( FC, "1", "0", left, FE ),
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( FD, "0", "1", left, FA ),
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( FD, "1", "1", left, FD ),
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( FE, "0", "1", stay, FH ),
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( FE, "1", "0", left, FA )
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),
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initialState = FA,
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finalStates = Set( FH ),
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blankSymbol = "0",
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inputTapeVals = Seq(),
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printEveryIter = 100000
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).run()
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}
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createIncrementMachine()
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createThreeStateBusyBeaver()
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// careful here, 47 mln iterations
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createFiveState2SymBusyBeaverMachine()
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}
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}
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