Turing machine #2

Merged
Simponic merged 4 commits from turing-machine into main 2023-10-25 01:44:38 -04:00
12 changed files with 10978 additions and 19675 deletions

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@ -23,6 +23,9 @@
<br /> <br />
📖 This page hosts strictly static content. 📖 This page hosts strictly static content.
<br /> <br />
🐙 Obviously my GitHub is at
<a href="https://github.com/Simponic">/simponic</a>.
<br />
🔔 My "real website" is at 🔔 My "real website" is at
<a href="https://simponic.xyz">simponic.xyz</a>. <a href="https://simponic.xyz">simponic.xyz</a>.
</h3> </h3>
@ -35,12 +38,23 @@
<div class="project-body"> <div class="project-body">
<h1>Euler Golf 2</h1> <h1>Euler Golf 2</h1>
<p> <p>
A puzzle game (with BFS solver) to explore rotations in the complex A puzzle game (with BFS solver) to explore rotations in the
plane. complex plane.
</p> </p>
</div> </div>
</a> </a>
<a class="project" href="/turing-machine/">
<div class="project-logo-container">
<i class="fa-solid fa-tape"></i>
</div>
<div class="project-body">
<h1>Simponic's State System</h1>
<p>A Turing Machine simulator specific to CS5000.</p>
</div>
</a>
<a class="project" href="/julia/"> <a class="project" href="/julia/">
<div class="project-logo-container"> <div class="project-logo-container">
<i class="fa-solid fa-square-root-variable"></i> <i class="fa-solid fa-square-root-variable"></i>
@ -77,8 +91,8 @@
<div class="project-body"> <div class="project-body">
<h1>The A-maze-ing Maize Maze</h1> <h1>The A-maze-ing Maize Maze</h1>
<p> <p>
A Randomized Kruskal's Maze game with (more) BFS. You play A Randomized Kruskal's Maze game with (more) BFS. You play as a
as a 🌽corn stalk trying to become 🍿popcorn. 🌽corn stalk trying to become 🍿popcorn.
</p> </p>
</div> </div>
</a> </a>
@ -90,9 +104,7 @@
<div class="project-body"> <div class="project-body">
<h1>Centipede</h1> <h1>Centipede</h1>
<p> <p>Boring remake of the classic arcade game.</p>
Boring remake of the classic arcade game.
</p>
</div> </div>
</a> </a>

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@ -3,7 +3,7 @@ const MAX_ZOOM = 4;
const C_THRESHOLD = Math.sqrt(2)/2; const C_THRESHOLD = Math.sqrt(2)/2;
const SLIDER_DIV = 2000*C_THRESHOLD; const SLIDER_DIV = 2000*C_THRESHOLD;
const gpu = new GPU(); const gpu = new GPUX();
const buildRender = (width, height) => gpu.createKernel(function (maxIterations, cr, ci, centerX, centerY, zoom, colorMultipliers) { const buildRender = (width, height) => gpu.createKernel(function (maxIterations, cr, ci, centerX, centerY, zoom, colorMultipliers) {
let zx = (this.output.x / this.output.y) * (centerX + (4 * this.thread.x / this.output.x - 2) * (zoom / 4)); let zx = (this.output.x / this.output.y) * (centerX + (4 * this.thread.x / this.output.x - 2) * (zoom / 4));
let zy = centerY + (4 * this.thread.y / this.output.y - 2) * (zoom / 4); let zy = centerY + (4 * this.thread.y / this.output.y - 2) * (zoom / 4);

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* {
margin: 0;
}
button {
background: #bbbbbb;
border: 1px solid white;
border-radius: 0.2rem;
padding: 0.3rem;
display: inline-block;
cursor: pointer;
}
button:hover {
background: #cccccc;
}
body {
font-family: "Trebuchet MS", sans-serif;
background-color: #aaaaaa;
}
.container {
display: flex;
width: 90%;
margin-left: auto;
margin-right: auto;
flex-direction: column;
gap: 1rem;
padding: 2rem;
}
.tape {
border-radius: 0.25rem;
box-shadow: 5px 5px 5px #666666;
display: flex;
padding: 1rem;
align-items: center;
gap: 1rem;
height: 5rem;
max-width: 100%;
border: 2px solid white;
overflow-x: scroll;
overflow-y: hidden;
}
.cell {
border-radius: 0.25rem;
box-shadow: 2px 2px 5px #666666;
background-color: #dddddd;
border: 2px solid white;
position: relative;
height: 80%;
transition: border 0.25s ease-in-out;
transition: background 0.25s ease-in-out;
display: flex;
flex-direction: column;
justify-content: center;
align-items: center;
flex: 1;
gap: 0.2rem;
padding: 0.2rem;
}
.circle {
position: absolute;
bottom: -15px;
left: 50%;
transform: translateX(-50%);
width: 10px;
height: 10px;
background-color: wheat;
border-radius: 50%;
opacity: 0.001;
transition: opacity 0.25s ease-in-out;
}
.cell.reading .circle {
opacity: 1;
}
.reading {
border-color: wheat;
background-color: wheat;
}
.cell-input {
border: none;
border-radius: 0.25rem;
background-color: 1px solid #ccc;
width: 50px;
margin-left: 0.25rem;
margin-right: 0.25rem;
text-align: center;
font-size: 1rem;
}
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flex-direction: column;
gap: 1rem;
box-shadow: 5px 5px 5px #666666;
border: 2px solid white;
border-radius: 0.25rem;
padding: 1rem;
}
textarea {
border-radius: 0.25rem;
height: 50vh;
}
.error {
color: red;
}
.success {
color: green;
}
.controls {
display: none;
gap: 1rem;
flex-direction: row;
justify-content: center;
align-items: stretch;
}
hr {
border-top: 2px solid black;
border-bottom: none;
}

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<!DOCTYPE html>
<html>
<head>
<title>Turing Machine Simulator</title>
<link rel="stylesheet" type="text/css" href="css/styles.css" />
<link rel="stylesheet" type="text/css" href="codemirror/codemirror.css" />
</head>
<body>
<div class="container">
<h1>Simponic's State System</h1>
<p><i>Developed for Kulyukin's CS5000</i></p>
<hr />
<p id="turing_state">State: _</p>
<div id="tape" class="tape"></div>
<div class="controls" id="controls">
<button id="toggle_play">🔁 Begin</button>
<button id="next_step">Next Step</button>
<button id="reset">Reset</button><br />
</div>
<div class="textarea-container">
<ul>
<li>
must have some instruction quadruple with the start state "q0"
</li>
<li>all computations will fail unless they end on the state "f"</li>
<li>
instructions are delimited with line breaks and are in the form
<i
>"< from_state > < read_symbol > < L/R/write_symbol > < to_state
>"</i
>
</li>
<li>comments ("//") are ignored</li>
</ul>
<textarea id="instructions">
// replaces 3 B's with "1"
q0 B 1 q1
q1 1 R q1
q1 B 1 q2
q2 1 R q2
q2 B 1 f</textarea
>
<div>
<button id="compile">Compile</button
><span style="margin-left: 0.5rem" id="compile_status"></span>
</div>
<div>
<button id="copy_state">Copy State</button>
</div>
</div>
</div>
<script src="codemirror/codemirror.js"></script>
<script src="js/observable.js"></script>
<script src="js/turing_machine.js"></script>
<script src="js/main.js"></script>
</body>
</html>

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const TAPE_LEN = 150;
const BLANK_VAL = "B";
const SIMULATION_INTERVAL = 200;
const MESSAGES = {
SET_CELL: "SET_CELL",
PAUSE: "PAUSE",
SIMULATE: "SIMULATE",
SET_READER: "SET_READER",
NEXT_STEP: "NEXT_STEP",
COMPILE: "COMPILE",
COMPILE_STATUS: "COMPILE_STATUS",
NEW_TURING_STATE: "NEW_TURING_STATE",
};
// -- the "real" code
const state = new Observable();
const inputCellId = (cellId) => `${cellId}-input`;
const cell = (cellId, initValue = "B") => {
const cellDiv = document.createElement("div");
cellDiv.classList.add("cell");
cellDiv.id = cellId;
const readingHead = document.createElement("div");
readingHead.classList.add("circle");
const input = document.createElement("input");
const inputId = inputCellId(cellId);
input.classList.add("cell-input");
input.id = inputId;
input.value = initValue;
input.addEventListener("focusin", () =>
state.notify({ type: MESSAGES.PAUSE })
);
input.addEventListener("focusout", () =>
state.notify({ type: MESSAGES.SET_CELL, cell: cellId, value: input.value })
);
const msgListener = (msg) => {
if (msg.type == MESSAGES.SET_CELL && msg.cell == cellId) {
input.value = msg.value;
}
if (msg.type == MESSAGES.SET_READER) {
if (msg.cell == cellId) {
cellDiv.classList.add("reading");
cellDiv.scrollIntoView({
behavior: "smooth",
});
} else cellDiv.classList.remove("reading");
}
if (msg.type == MESSAGES.COMPILE) {
state.unsubscribe(msgListener);
}
};
state.subscribe(msgListener);
cellDiv.appendChild(input);
cellDiv.appendChild(readingHead);
return cellDiv;
};
const parseRules = (rules, beginState) => {
const quadruples = rules.split("\n");
const instructions = [];
quadruples.forEach((quadruple, line) => {
const commentLess = quadruple.replaceAll(/\/\/.*/g, "").trim();
if (!commentLess) {
return;
}
const items = commentLess
.split(" ")
.map((x) => x.trim())
.filter((x) => x);
if (items.length != 4) {
throw new Error(`Invalid instruction on line ${line + 1}`);
}
instructions.push(items);
});
if (!instructions.some(([fromState]) => fromState == beginState)) {
throw new Error(
`At least one instruction must begin from state: ${beginState}`
);
}
return instructions;
};
// -- a bit of some hacky ui code --
const tapeEl = document.getElementById("tape");
const compileButton = document.getElementById("compile");
const resetButton = document.getElementById("reset");
const controlsEl = document.getElementById("controls");
const nextStepButton = document.getElementById("next_step");
const togglePlayButton = document.getElementById("toggle_play");
const compileStatusEl = document.getElementById("compile_status");
const turingMachineStateEl = document.getElementById("turing_state");
const copyStateButton = document.getElementById("copy_state");
// init instructions from params
const instructionsEl = document.getElementById("instructions");
const editorEl = CodeMirror.fromTextArea(instructionsEl, {
lineNumbers: true,
});
const urlParams = new URLSearchParams(window.location.search);
if (urlParams.get("instructions")) {
editorEl.setValue(atob(urlParams.get("instructions")));
}
[compileButton, resetButton].forEach((button) =>
button.addEventListener("click", () => {
state.notify({ type: MESSAGES.PAUSE });
state.notify({ type: MESSAGES.COMPILE, value: editorEl.getValue() });
})
);
nextStepButton.addEventListener("click", () => {
state.notify({ type: MESSAGES.PAUSE });
state.notify({ type: MESSAGES.NEXT_STEP });
});
// hackily copy the program state and put it in the clipboard
copyStateButton.addEventListener("click", () => {
const start = Array(TAPE_LEN)
.fill(BLANK_VAL)
.map((blank, i) => document.getElementById(inputCellId(i))?.value ?? blank)
.join("")
.replaceAll(new RegExp(`(${BLANK_VAL})*\$`, "g"), "");
const instructions = btoa(editorEl.getValue());
navigator.clipboard
.writeText(
window.location.href.split("?")[0] +
`?start=${start}&instructions=${instructions}`
)
.then(() => alert("copied to clipboard"));
});
// simulate / pause button
let playButton_simulationStatus = "paused";
togglePlayButton.addEventListener("click", function () {
if (playButton_simulationStatus == "paused") {
state.notify({ type: MESSAGES.SIMULATE });
} else if (playButton_simulationStatus == "simulate") {
state.notify({ type: MESSAGES.PAUSE });
}
});
state.subscribe((msg) => {
if (msg.type == MESSAGES.PAUSE) {
togglePlayButton.innerHTML = "🔁 Begin";
playButton_simulationStatus = "paused";
}
if (msg.type == MESSAGES.SIMULATE) {
togglePlayButton.innerHTML = "⏸️ Pause";
playButton_simulationStatus = "simulate";
}
});
state.subscribe((msg) => {
if (msg.type == MESSAGES.COMPILE_STATUS) {
const { error, success } = msg;
if (error) {
compileStatusEl.classList.remove("success");
compileStatusEl.classList.add("error");
compileStatusEl.innerHTML = error;
}
if (success) {
compileStatusEl.classList.add("success");
compileStatusEl.classList.remove("error");
compileStatusEl.innerHTML = `Successful compile at ${new Date().toLocaleString()}!`;
}
}
});
state.subscribe((msg) => {
if (msg.type == MESSAGES.COMPILE_STATUS) {
const { error, success } = msg;
if (error) {
controlsEl.style.display = "none";
} else if (success) {
controlsEl.style.display = "flex";
}
}
});
state.subscribe((msg) => {
if (msg.type == MESSAGES.NEW_TURING_STATE) {
turingMachineStateEl.innerHTML = msg.value;
}
});
// -
const main = () => {
let turingMachine;
const startString = urlParams.get("start");
state.subscribe((msg) => {
if (msg.type == MESSAGES.SET_CELL) {
const { value, cell } = msg;
if (turingMachine) turingMachine.setTapeAtCell(cell, value);
}
if (msg.type == MESSAGES.COMPILE) {
const { value } = msg;
try {
const beginState = "q0";
const acceptState = "f";
const tape = Array(TAPE_LEN)
.fill(BLANK_VAL)
.map((x, i) =>
startString && i < startString.length ? startString[i] : x
);
// put the cells into the tape
const cells = tape.map((_, cellId) => cell(cellId, tape[cellId]));
tapeEl.innerHTML = "";
for (const cell of cells) {
tapeEl.appendChild(cell);
}
const rules = parseRules(value, beginState, acceptState);
turingMachine = new TuringMachine(tape, rules, beginState, acceptState);
state.notify({ type: MESSAGES.SET_READER, cell: 0 });
state.notify({
type: MESSAGES.NEW_TURING_STATE,
value: turingMachine.getStateStatus(),
});
state.notify({ type: MESSAGES.COMPILE_STATUS, success: true });
} catch (e) {
state.notify({ type: MESSAGES.COMPILE_STATUS, error: e.toString() });
}
}
if (msg.type == MESSAGES.SIMULATE) {
const interval = setInterval(() => {
state.notify({ type: MESSAGES.NEXT_STEP });
}, SIMULATION_INTERVAL);
const subscriptionFn = (msg) => {
if (msg.type == MESSAGES.PAUSE) {
clearInterval(interval);
state.unsubscribe(subscriptionFn);
}
};
state.subscribe(subscriptionFn);
}
if (msg.type == MESSAGES.NEXT_STEP && turingMachine) {
const step = turingMachine.step();
const status = turingMachine.getStateStatus();
const cell = turingMachine.getHead();
if (!step) {
const accepting = turingMachine.isAccepting();
state.notify({
type: MESSAGES.NEW_TURING_STATE,
value: accepting
? `<span class='success'>Accept(${status})</span>`
: `<span class='error'>Fail(${status})</span>`,
});
} else {
state.notify({
type: MESSAGES.NEW_TURING_STATE,
value: status,
});
}
state.notify({
type: MESSAGES.SET_READER,
cell,
});
state.notify({
type: MESSAGES.SET_CELL,
cell,
value: turingMachine.getTapeAtCell(cell),
});
if (!step)
state.notify({
type: MESSAGES.PAUSE,
});
}
});
};
main();

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@ -0,0 +1,14 @@
class Observable {
constructor() {
this.observers = [];
}
subscribe(f) {
this.observers.push(f);
}
unsubscribe(f) {
this.observers = this.observers.filter((subscriber) => subscriber !== f);
}
notify(data) {
this.observers.forEach((observer) => observer(data));
}
}

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@ -0,0 +1,72 @@
class TuringMachine {
constructor(tape = [], rules = [], initialState = "q0", acceptState = "f") {
this.tape = tape;
this.rules = this.parseRules(rules);
this.state = initialState;
this.head = 0;
this.acceptState = acceptState;
this.iteration = 0;
}
getStateStatus() {
return `State: ${this.state}, Step: ${this.iteration}`;
}
getHead() {
return this.head;
}
getState() {
return this.state;
}
getTapeAtCell(idx) {
return this.tape[idx];
}
setTapeAtCell(idx, val) {
this.tape[idx] = val;
}
isAccepting() {
return this.state == this.acceptState;
}
parseRules(rules) {
const parsedRules = {};
for (const [currentState, readSymbol, action, newState] of rules) {
const key = `${currentState},${readSymbol}`;
const value = `${newState},${action}`;
parsedRules[key] = value;
}
return parsedRules;
}
step() {
const currentSymbol = this.tape[this.head];
const key = `${this.state},${currentSymbol}`;
if (!(key in this.rules)) {
return false;
}
const rule = this.rules[key];
const [newState, action] = rule.split(",");
this.state = newState;
this.iteration++;
if (action === "R") {
this.head += 1;
} else if (action === "L") {
this.head -= 1;
} else {
this.tape[this.head] = action;
}
if (this.isAccepting()) {
return false;
}
return this.head >= 0 && this.head < this.tape.length;
}
}