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Builder.js
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Builder.js
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"use strict";
/**
* Created by sdiemert on 2017-03-14.
*/
const QTM = require("./QTM").QTM;
const fs = require("fs");
const csv = require("csv-parse/lib/sync");
const math = require("mathjs");
/**
* Counts the number of unqiue states the machine has.
*
* @param A {Array} 2D array representing the machine spec.
*
* @return {number} the number of unqiue states in the machine spec.
*/
function countStates(A){
const Q = [];
for(let i = 0; i < A.length; i++){
let x = A[i][0];
if(Q.indexOf(x) < 0){
Q.push(x);
}
}
return Q.length;
}
/**
* Builds a QTM from a csv text blob.
* @param S {string}
* @param tapeSize {number}
* @param base {number=3}
* @returns {QTM}
*/
function machineFromBlob(S, tapeSize, base){
return buildMachine(csv(cleanMachineSpecification(S)), tapeSize, base);
}
/**
* Makes a QTM from the input 2D array
* @param M {Array} contains the specification for the QTM
* @param Nt {number} number of cells in the tape
* @param base {number} number of tape symbols
*/
function buildMachine(M, Nt, base){
const S = [];
for(let i = 0; i < M.length; i++){
let q1 = parseInt(M[i][0]);
let r = parseInt(M[i][1]);
let w = parseInt(M[i][2]);
let m = parseInt(M[i][3]);
let q2 = parseInt(M[i][4]);
let a = math.complex(M[i][5]);
S.push([q1, r, w, m, q2, a]);
}
const Ns = countStates(S);
const Nx = math.pow(base, Nt) * Ns * Nt;
console.log("Building machine, state size:", Ns, "tape size:", Nt, "Size: ", Nx);
let U = math.zeros(Nx, Nx);
for(let i = 0; i < S.length; i++){
U = math.sparse(math.add(U, makeTransferMatrix(S[i][0], S[i][1], S[i][2], S[i][4], S[i][3], Nt, Ns, S[i][5], Nx)));
}
//console.log("Unitary?", checkUnitary(U, Ns, Nt));
var Q = new QTM(math.matrix(U, 'sparse'), Ns, 0, Nt, getLastState(S));
//console.log("New machine: " + Q.toString());
return Q;
}
function getLastState(S){
let maxVal = S[0][0];
for(let i = 0; i < S.length; i++){
if(S[i][0] > maxVal) maxVal = S[i][0];
}
return maxVal;
}
/**
*
* @param fname {string}
*/
function machineFromMatrixFile(fname){
/** @type {QTM} */
const M = JSON.parse(fs.readFileSync(fname, 'utf-8'));
const U = math.matrix(math.complex(M.U.data), 'sparse');
return new QTM(U, M.numStates, M.start, M.tapeLength, M.halt);
}
/**
* @param fname {string} the name of the file
* @param Nt {number} number of cells on the machine's tape
* @param base {number} size of machine alphabet
* @param writeMatrix {boolean} if we should write the resulting machine's matrix to a file for saving later.
* @returns {QTM} the built QTM.
*/
function machineFromFile(fname, Nt, base, writeMatrix){
let matrixRegex = /\.matrix/;
let csvRegex = /\.csv/;
if(matrixRegex.exec(fname)){
return machineFromMatrixFile(fname);
}else if(csvRegex.exec(fname)){
// read file and remove duplicate new line characters.
const M = machineFromBlob(fs.readFileSync(fname, "utf-8"), Nt, base);
//write machine to file for speed later.
if(writeMatrix) fs.writeFileSync(fname.replace(/\.csv/g, ".matrix"), JSON.stringify(M), 'utf-8');
return M;
}else{
return null; // nothing found.
}
}
/**
* Cleans the machine specification before CSV parsing, removes comments
* and extra white spaces.
* @param S {string} the machine specification blob to the cleaned.
*/
function cleanMachineSpecification(S){
return S.replace(/;.*\n/g, "")
.replace(/\n\n/g, "\n")
.replace(/#/g, "2")
.toUpperCase()
.replace(/L/g, "-1")
.replace(/R/g, "1");
}
/**
* Makes a transfer matrix for the command
* @param q1 {number} initial state
* @param r {number} read the value on cell - 0,1,2
* @param w {number} write the value to the cell - 0,1,2
* @param m {number} move -1, 0, 1
* @param q2 {number} next state
* @param I {number} number of tape cells
* @param Q {number} number of machine states
* @param a {math.Complex} transition weight
* @param x {number} rows and cols of square matrix
*/
function makeTransferMatrix(q1, r, w, m, q2, I, Q, a, x){
//console.log(q1, r, w, m, q2, I ,Q, a, x);
let U = math.zeros(x,x, 'sparse');
let i,k,z, b0, b1, cx, c0, rx, r1, ip3, Ip3;
for(i = 0; i < I; i++){
// cache some frequently computed values...
ip3 = math.pow(3,i);
Ip3 = math.pow(3,I);
b0 = Ip3*Q*i + q1 * Ip3; // base of starting state
b1 = Ip3*Q*(i+m) + q2 * Ip3; // base of terminating state
for(z=0; z < math.pow(3, I-i-1); z++){
for(k = 0; k < ip3; k++){
cx = k + 3 * ip3* z + r * ip3;
c0 = b0 + cx;
rx = k + 3 * ip3 * z + w * ip3;
r1 = b1 + rx;
//console.log(r1, c0, a);
if(r1 >= x || r1 < 0){
//console.log("overflow", r1, c0, a);
U = math.subset(U, math.index(c0, c0), 0);
}else{
U = math.subset(U, math.index(r1, c0), a);
}
}
}
}
return U;
}
/**
*
* @param U {Matrix}
* @param t {number}
* @param q {number}
*/
function checkUnitary(U, q, t){
console.log("checking unitary...");
const Up = math.matrix(math.transpose(math.conj(U)), 'sparse');
console.log("found conj transpose");
const X = math.multiply(Up, U);
console.log("found result"); /*
/*
We can only consider the first t-1 cells of the tape,
the last cell will have invalid movements due to the machine
actually needing an infinite tape....
*/
let Su = "";
for(var i = 0; i < X.size()[0]; i++){
for(var j = 0; j < X.size()[0]; j++){
Su += math.subset(U, math.index(i,j)) +" ";
}
Su += "\n";
}
fs.writeFileSync('matrix.txt', Su, 'utf-8');
const R = math.range(0, math.pow(3, t-1) * (t-1) * q);
const Xs = math.subset(X, math.index(R, R));
return math.deepEqual(Xs, math.eye(R.size()[0]));
}
/**
*
* @param U {math.Matrix}
*
* @return {boolean}
*/
function checkMatrixAmplitudes(U){
const s = U.size()[0];
let rowSum, v;
for(let i = 0; i < s; i++){
rowSum = 0;
for(let j = 0; j < s; j++){
v = math.complex(math.subset(U, math.index(i,j)));
rowSum += math.pow(v.re, 2) + math.pow(v.im, 2);
}
if(rowSum > 1) return false;
}
return true;
}
module.exports = {
buildMachine : buildMachine,
machineFromFile : machineFromFile,
machineFromBlob : machineFromBlob
};