private static void CreateOneTapeUnaryMultiplicationStates(TuringMachine tm)
{
var Q0 = tm.CreateState();
var Q1 = tm.CreateState();
var Q2 = tm.CreateState();
var Q3 = tm.CreateState();
var Q4 = tm.CreateState();
var Q5 = tm.CreateState();
var Q6 = tm.CreateState();
var Q7 = tm.CreateState();
var Q8 = tm.CreateState();
var Q9 = tm.CreateState();
var Q10 = tm.CreateState();
var Q11 = tm.CreateState();
var QE1 = tm.CreateAcceptingState();
var QE2 = tm.CreateAcceptingState();
Q0.AddTransition("0/_,R", Q1);
Q0.AddTransition("1/_,R", QE1);
QE1.AddTransition("0/_,R");
Q1.AddTransition("0/_,R", Q2);
Q1.AddTransition("1/_,R", QE2);
QE2.AddTransition("X/0,R");
Q2.AddTransition("0/0,R");
Q2.AddTransition("1/1,R", Q3);
Q3.AddTransition("X/X,R");
Q3.AddTransition("1/1,R");
Q3.AddTransition("_/_,L", Q10);
Q3.AddTransition("0/0,R", Q11);
Q11.AddTransition("0/0,R");
Q11.AddTransition("X/X,L", Q10);
Q11.AddTransition("_/_,L", Q10);
Q10.AddTransition("0/X,R", Q4);
Q10.AddTransition("1/1,L", Q7);
Q4.AddTransition("X/X,R");
Q4.AddTransition("0/0,R");
Q4.AddTransition("_/0,L", Q5);
Q5.AddTransition("0/0,L");
Q5.AddTransition("X/X,L", Q6);
Q6.AddTransition("X/X,L");
Q6.AddTransition("0/0,L", Q3);
Q6.AddTransition("1/1,L", Q7);
Q7.AddTransition("0/0,L");
Q7.AddTransition("_/_,R", Q1);
}
private static void CreateUltimateUnaryMultiplicationStates(TuringMachine tm)
{
var Q0 = tm.CreateState();
var Q1 = tm.CreateState();
var Q2 = tm.CreateState();
var Q3 = tm.CreateState();
var Q4 = tm.CreateState();
var Q5 = tm.CreateState();
var Q6 = tm.CreateState();
var Q7 = tm.CreateState();
var Q8 = tm.CreateState();
var Q9 = tm.CreateState();
var Q10 = tm.CreateState();
var QE = tm.CreateAcceptingState();
//0*x=0
Q0.AddTransition("1**/_**,RSS", Q1);
Q1.AddTransition("0**/0**,RSS");
Q1.AddTransition("_**/_**,SSS", QE);
//1*x=x
Q0.AddTransition("0**/_1*,RLS", Q2);
Q2.AddTransition("1**/_**,RSS", Q3);
Q3.AddTransition("0**/0*0,RSL");
Q3.AddTransition("_**/_**,SRR", QE);
//y*x -- 1 not yet consumed.
Q2.AddTransition("0**/_00,RLL", Q4);
Q4.AddTransition("0**/_00,RLL");
//y*0=0
Q4.AddTransition("1**/_*0,RRL", Q5);
Q5.AddTransition("_**/_**,SSR", Q6);
Q6.AddTransition("**0/**_,SSR");
Q6.AddTransition("**_/**_,SSS", QE);
//y*(1+?)
Q5.AddTransition("00*/01*,RSS", Q7);
//y*1=y
// Q5.AddTransition("_**/_**,SSS", Q6);
// Q6.AddTransition("*0*/*00,SRL");
// Q6.AddTransition("*1*/*10,SRS", QE);
//Trivial cases covered
//y*x| y>1 & x>1
// Q5.AddTransition("00*/000,SRL");
// Q5.AddTransition("01*/010,SSL", Q9);
Q7.AddTransition("01*/010,RRL", Q8);
Q7.AddTransition("_1*/_1*,SSR", QE);
Q8.AddTransition("*0*/*00,SRL");
Q8.AddTransition("01*/010,SSL", Q9);
Q8.AddTransition("_1*/_10,SRS", QE);
Q9.AddTransition("01*/010,RLL", Q10);
Q9.AddTransition("_1*/_1*,SRR", QE);
Q10.AddTransition("*0*/*00,SLL");
Q10.AddTransition("01*/*10,SSL", Q7);
Q10.AddTransition("_1*/_10,SSS", QE);
}
private static void CreateBestUnaryMultiplicationStates(TuringMachine tm)
{
var Q0 = tm.CreateState();
var Q1OnePlusTimesX = tm.CreateState();
var Q2OneTimesX = tm.CreateState();
var Q3YTimesX = tm.CreateState();
var Q4YTimesX = tm.CreateState();
var Q5 = tm.CreateState();
var Q6YTimesOne = tm.CreateState();
var Q7 = tm.CreateState();
var Q8 = tm.CreateState();
var Q9 = tm.CreateState();
var Q10 = tm.CreateState();
var QE = tm.CreateAcceptingState();
//0*x=0
Q0.AddTransition("1**/1**,SSS", QE);
//1*x=x
Q0.AddTransition("0**/_1*,RLS", Q1OnePlusTimesX);
Q1OnePlusTimesX.AddTransition("1**/_**,RSL", Q2OneTimesX);
Q2OneTimesX.AddTransition("0**/0*0,RSL");
Q2OneTimesX.AddTransition("_**/_**,SSR", QE);
//y*x -- 1 not yet consumed.
Q1OnePlusTimesX.AddTransition("0**/_0*,RLS", Q3YTimesX);
Q3YTimesX.AddTransition("0**/_0*,RLS");
Q3YTimesX.AddTransition("1**/_**,RRS", Q4YTimesX);
//y*0=0
Q4YTimesX.AddTransition("_**/_**,SSS", QE);
//y*(1+?)
Q4YTimesX.AddTransition("00*/010,RRL", Q5);
//y*1=y
Q5.AddTransition("_**/_**,SSS", Q6YTimesOne);
Q6YTimesOne.AddTransition("*0*/*00,SRL");
Q6YTimesOne.AddTransition("*1*/*10,SRL", QE);
//Trivial cases covered
//y*x| y>1 & x>1
Q5.AddTransition("00*/000,SRL");
Q5.AddTransition("01*/010,SSL", Q9);
Q7.AddTransition("01*/010,RRL", Q8);
Q7.AddTransition("_1*/_1*,SRR", QE);
Q8.AddTransition("*0*/*00,SRL");
Q8.AddTransition("*1*/*10,SSL", Q9);
Q9.AddTransition("01*/010,RLL", Q10);
Q9.AddTransition("_1*/_1*,SRR", QE);
Q10.AddTransition("*0*/*00,SLL");
Q10.AddTransition("01*/*10,SSL", Q7);
Q10.AddTransition("_1*/_10,SRL", QE);
}
private static void CreateImprovedUnaryMultiplicationStates(TuringMachine tm)
{
var Q0 = tm.CreateState();
var Q1OnePlusTimesX = tm.CreateState();
var Q2OneTimesX = tm.CreateState();
var Q3YTimesX = tm.CreateState();
var Q4YTimesX = tm.CreateState();
var Q5 = tm.CreateState();
var Q6YTimesOne = tm.CreateState();
var Q7FromLeft = tm.CreateState();
var Q8FromRight = tm.CreateState();
var QE = tm.CreateAcceptingState();
//0*x=0
Q0.AddTransition("1**/1**,SSS", QE);
//1*x=x
Q0.AddTransition("0**/_0*,RLS", Q1OnePlusTimesX);
Q1OnePlusTimesX.AddTransition("1**/_**,RSL", Q2OneTimesX);
Q2OneTimesX.AddTransition("0**/0*0,RSL");
Q2OneTimesX.AddTransition("_**/_**,SSR", QE);
//y*x -- 1 not yet consumed.
Q1OnePlusTimesX.AddTransition("0**/_0*,RLS", Q3YTimesX);
Q3YTimesX.AddTransition("0**/_0*,RLS");
Q3YTimesX.AddTransition("1**/_**,RSS", Q4YTimesX);
//y*0=0
Q4YTimesX.AddTransition("_**/_**,SSS", QE);
//y*(1+?)
Q4YTimesX.AddTransition("0_*/0_*,RRS", Q5);
//y*1=y
Q5.AddTransition("_**/_**,SSS", Q6YTimesOne);
Q6YTimesOne.AddTransition("*0*/*00,SRL");
Q6YTimesOne.AddTransition("*_*/*_*,SLR", QE);
//Trivial cases covered
//y*x| y>1 & x>1
Q5.AddTransition("*0*/*00,SRL", Q7FromLeft);
//Left 2 right
Q7FromLeft.AddTransition("__*/__*,SSR", QE);
Q7FromLeft.AddTransition("*0*/*00,SRL");
Q7FromLeft.AddTransition("0_*/0_*,RLS", Q8FromRight);
//Right 2 left
Q8FromRight.AddTransition("__*/__*,SSR", QE);
Q8FromRight.AddTransition("*0*/*00,SLL");
Q8FromRight.AddTransition("0_*/0_*,RRS", Q7FromLeft);
}
private static void CreateUnaryMultiplicationStates(TuringMachine tm)
{
var Q0 = tm.CreateState();
var Q1 = tm.CreateState();
var Q2 = tm.CreateState();
var Q3 = tm.CreateState();
var QE = tm.CreateAcceptingState();
// q0: Übertrage ersten Faktor auf Band 2
Q0.AddTransition("0**/_0*,RLS", Q0);
Q0.AddTransition("1**/_**,RRS", Q1);
// q1: Überprüfe, ob noch eine Stelle des ersten Faktors zu verarbeiten ist
Q1.AddTransition("0**/0**,RSS", Q2);
Q1.AddTransition("_**/_**,SSS", QE);
// q2: Addiere Band 2 auf Band 3
Q2.AddTransition("*0_/*00,SRR", Q2);
Q2.AddTransition("*_*/*_*,SLS", Q3);
// q3: Rücke zum Anfang des ersten Faktors
Q3.AddTransition("*0*/*0*,SLS", Q3);
Q3.AddTransition("*_*/*_*,SRS", Q1);
}