automata/web/root/src/examples.ts
2026-04-09 12:22:46 -04:00

507 lines
11 KiB
TypeScript

import { bus } from "./bus.ts";
export type Category =
| "Tutorial"
| "DFA"
| "NFA"
| "DPDA"
| "NPDA"
| "TM"
| "NTM"
| "CFG";
export class Example {
readonly category: Category;
readonly title: string;
readonly machine: string;
constructor(category: Category, title: string, machine: string) {
this.category = category;
this.title = title;
this.machine = machine;
}
}
export const examples: readonly Example[] = [
new Example(
"Tutorial",
"DFA",
`// strings over a,b which start and end with different letters
type = DFA // type of machine DFA, NFA, DPDA, NPDA, DTM, NTM
Q = {q0, qa, qa', qb, qb'} // set of states
E = {a, b} // alphabet
F = {qa', qb'} // set of final states
q0 = q0 // initial state
// transition function (state, letter) -> state
d(q0, a) = qa
d(q0, b) = qb
d(qa, a) = qa
d(qa, b) = qa'
d(qa', a) = qa
d(qa', b) = qa'
d(qb, a) = qb'
d(qb, b) = qb
d(qb', a) = qb'
d(qb', b) = qb`,
),
new Example(
"Tutorial",
"NFA",
`// strings of 1's whos length is divisible by two or three and longer than 1
type = NFA // type of machine
Q = {q0, q2, q2f, q3, q3', q3f} // set of states
E = {1} // alphabet
F = {q2f, q3f} // set of final states
q0 = q0 // initial state
// transition function (state, letter) -> state
// non deterministic part
d(q0, 1) = q2
d(q0, 1) = q3
d(q2, 1) = q2f
d(q2f, 1) = q2
d(q3, 1) = q3'
d(q3', 1) = q3f
d(q3f, 1) = q3
`,
),
new Example(
"Tutorial",
"NFA with epsilon",
`// strings containing only all a's, or all b's, or all c's
type = NFA // type of machine
Q = {q0, qa, qb, qc} // set of states
E = {a, b, c} // alphabet
F = {qa, qb, qc} // set of final states
q0 = q0 // initial state
// transition function (state, letter) -> state
// non deterministic part
d(q0, epsilon) = qa
d(q0, epsilon) = qb
d(q0, epsilon) = qc
d(qa, a) = qa
d(qb, b) = qb
d(qc, c) = qc
`,
),
new Example(
"Tutorial",
"DPDA Final State",
`// Accept strings over a,b of the form a^nb^k where n != k and n,k > 0
type = DPDA
Q = {q0, qas, qeq, qmb, qlb} // states
E = {a, b} // alphabet
T = {z0, A} // stack
F = {qmb, qlb} // final states
accept = F // accept by final state
q0 = q0
z0 = z0
d(q0, a, z0) = (qas, z0)
d(qas, a, z0) = (qas, [A z0])
d(qas, b, z0) = (qeq, z0)
d(qas, a, A) = (qas, [A A])
d(qas, b, A) = (qlb, ~)
d(qlb, b, A) = (qlb, ~)
d(qlb, b, z0) = (qeq, z0)
d(qeq, b, z0) = (qmb, z0)
d(qmb, b, z0) = (qmb, z0)`,
),
new Example(
"Tutorial",
"DPDA Empty Stack",
`// Accept strings over a,b which are of form a^n b^n
type = DPDA
Q = {qa, qb} // states
E = {a, b} // alphabet
T = {Z0, A} // stack
accept = N // accept by empty stack
q0 = qa
z0 = Z0
// build stack of A's (equal to a's encountered)
d(qa, a, Z0) = (qa, [A Z0])
d(qa, a, A) = (qa, [A A])
// transition to b state once a b is encountered
d(qa, b, A) = (qb, ~)
// consume b's until A's run out
d(qb, b, A) = (qb, ~)`,
),
// new Example(
// "Tutorial",
// "NPDA Final State",
// ``,
// ),
new Example(
"Tutorial",
"NPDA Empty Stack",
`// Accept all strings over a,b which are spelt the same backwards and forwards
type=NPDA
Q = {q0, q1} // states
E = {a, b} // alphabet
T = {Z0, A, B} // stack
accept = E // accept by empty stack
q0 = q0
z0 = Z0
// push letters we see to stack
d(q0, a, Z0) = (q0, [A Z0])
d(q0, b, Z0) = (q0, [B Z0])
d(q0, a, A) = (q0, [A A])
d(q0, b, A) = (q0, [B A])
d(q0, a, B) = (q0, [A B])
d(q0, b, B) = (q0, [B B])
// transition to q1
// even
d(q0, epsilon, Z0) = { (q1, Z0) }
d(q0, epsilon, A) = { (q1, A) }
d(q0, epsilon, B) = { (q1, B) }
// odd
d(q0, a, Z0) = { (q1, Z0) }
d(q0, a, A) = { (q1, A) }
d(q0, a, B) = { (q1, B) }
d(q0, b, Z0) = { (q1, Z0) }
d(q0, b, A) = { (q1, A) }
d(q0, b, B) = { (q1, B) }
// consume stack until empty
d(q1, a, A) = { (q1, epsilon) }
d(q1, b, B) = { (q1, epsilon) }`,
),
new Example(
"Tutorial",
"TM",
`// Accept strings over a,b,c of the form a^n b^n c^n, n > 0
type = TM
Q = {q1, q2, q3, q4, q5, q6, qf} // states
T = {a, b,c, B, X, Y, Z} // stack
F = {qf} // final states
q0 = q1
B = B
d(q1, a) = (q2, X, R)
d(q1, Y) = (q5, Y, R)
d(q2, a) = (q2, a, R)
d(q2, b) = (q3, Y, R)
d(q2, Y) = (q2, Y, R)
d(q3, b) = (q3, b, R)
d(q3, c) = (q4, Z, L)
d(q3, Z) = (q3, Z, R)
d(q4, a) = (q4, a, L)
d(q4, b) = (q4, b, L)
d(q4, X) = (q1, X, R)
d(q4, Y) = (q4, Y, L)
d(q4, Z) = (q4, Z, L)
d(q5, Y) = (q5, Y, R)
d(q5, Z) = (q6, Z, R)
d(q6, B) = (qf, B, R)
d(q6, Z) = (q6, Z, R)`,
),
// new Example(
// "Tutorial",
// "NTM",
// ``,
// ),
new Example(
"DFA",
"modulo",
`type=DFA
E={1,2,3}
Q={q0, q1, q2, q3, q4}
F = {q0}
q0=q0
d(q0, 1) = q1
d(q1, 1) = q2
d(q2, 1) = q3
d(q3, 1) = q4
d(q4, 1) = q0
d(q0, 2) = q2
d(q1, 2) = q3
d(q2, 2) = q4
d(q3, 2) = q0
d(q4, 2) = q1
d(q0, 3) = q3
d(q1, 3) = q4
d(q2, 3) = q0
d(q3, 3) = q1
d(q4, 3) = q2`,
),
new Example(
"DPDA",
"unequal",
`type = DPDA
Q = {q0, qas, qeq, qmb, qlb} // states
E = {a, b} // alphabet
T = {z0, A} // stack
F = {qmb, qlb} // final states
accept = F // accept by final state
q0 = q0
z0 = z0
d(q0, a, z0) = (qas, z0)
d(qas, a, z0) = (qas, [A z0])
d(qas, b, z0) = (qeq, z0)
d(qas, a, A) = (qas, [A A])
d(qas, b, A) = (qlb, ~)
d(qlb, b, A) = (qeq, ~)
d(qlb, b, z0) = (qeq, z0)
d(qeq, b, z0) = (qmb, z0)
d(qmb, b, z0) = (qmb, z0)`,
),
new Example(
"NPDA",
"palindrome",
`type=NPDA
Q = {q0, q1} // states
E = {a, b} // alphabet
T = {z0, A, B} // stack
accept = E // accept by empty stack
q0 = q0
z0 = z0
// push letters we see to stack
d(q0, a, z0) = (q0, [A z0])
d(q0, b, z0) = (q0, [B z0])
d(q0, a, A) = (q0, [A A])
d(q0, b, A) = (q0, [B A])
d(q0, a, B) = (q0, [A B])
d(q0, b, B) = (q0, [B B])
// transition to q1
// even
d(q0, epsilon, z0) = { (q1, z0) }
d(q0, epsilon, A) = { (q1, A) }
d(q0, epsilon, B) = { (q1, B) }
// odd
d(q0, a, z0) = { (q1, z0) }
d(q0, a, A) = { (q1, A) }
d(q0, a, B) = { (q1, B) }
d(q0, b, z0) = { (q1, z0) }
d(q0, b, A) = { (q1, A) }
d(q0, b, B) = { (q1, B) }
// consume stack until empty
d(q1, a, A) = { (q1, epsilon) }
d(q1, b, B) = { (q1, epsilon) }`,
),
new Example(
"NPDA",
"kleen star stack",
`type=NPDA
Q = {q0, q1} // states
E = {a, b} // alphabet
T = {z0, A, B} // stack
accept = E // accept by empty stack
q0 = q0
z0 = z0
// construct all possible permutations of A's and B's
d(q0, epsilon, z0) = { (q0, [A z0]), (q0, [B z0]) }
d(q0, epsilon, A) = { (q0, [A A]), (q0, [B A]) }
d(q0, epsilon, B) = { (q0, [A B]), (q0, [B B]) }
// transition to q1
d(q0, epsilon, z0) = { (q1, z0) }
d(q0, epsilon, A) = { (q1, A) }
d(q0, epsilon, B) = { (q1, B) }
// consume stack until empty
d(q1, a, A) = { (q1, epsilon) }
d(q1, b, B) = { (q1, epsilon) }`,
),
new Example("TM", "a^nb^n",
`// accepts all strings on {a,b}+ of the form anbn
type = TM
Q = { q0, q1, q2, q3, q4 } // set of internal states
F = { q4 } // set of final states
T = { a, b, X, Y, B } // tape alphabet
B = B // the blank symbol (tape initializer symbol)
q0 = q0 // initial state
d(q0,a)=(q1,x,R)
d(q1,a)=(q1,a,R)
d(q1,Y)=(q1,y,R)
d(q1,b)=(q2,y,L)
d(q2,Y)=(q2,y,L)
d(q2,a)=(q2,a,L)
d(q2,X)=(q0,x,R)
d(q0,Y)=(q3,y,R)
d(q3,Y)=(q3,y,R)
d(q3,B)=(q4,B,R)
`),
// new Example("CFG", "definition",
// `// CFG's aren't supported yet, and this definition is not complete.
// // This is the definition for the grammar the definition has itself
// type=CFG
// S -> TopLevel | TopLevel S
// TopLevel -> Ident "=" Item // Item
// TopLevel -> Ident Tuple "=" Item // Transition Functions
// TopLevel -> Production | Table
// Item -> Symbol | String | Tuple | List
// Symbol -> Ident | "~"
// String -> "\"" "\""
// Tuple -> "(" ItemList ")"
// List -> "{" ItemList "}" | "[" ItemList "]"
// ItemList -> ~ | Item ItemList | Item "," ItemList
// Production -> ProductionGroup "->" ProductionGroupList
// ProductionGroupList -> ProductionGroup | ProductionGroupList "|" ProductionGroup
// ProductionGroup -> ProductionUnit | ProductionGroup ProductionUnit
// ProductionUnit -> Ident | "~" | String
// `)
];
const CATEGORY_ORDER: Category[] = [
"Tutorial",
"DFA",
"NFA",
"DPDA",
"NPDA",
"TM",
"NTM",
"CFG",
];
function buildExamplesDropdown(
selectEl: HTMLSelectElement,
examples: readonly Example[],
onPick?: (ex: Example) => void,
) {
// Clear everything except the first placeholder option (if present)
const keepFirstPlaceholder = selectEl.options.length > 0 &&
selectEl.options[0].disabled && selectEl.options[0].value === "";
selectEl.innerHTML = "";
if (keepFirstPlaceholder) {
const placeholder = document.createElement("option");
placeholder.value = "";
placeholder.disabled = true;
placeholder.selected = true;
placeholder.textContent = "Choose an example…";
selectEl.appendChild(placeholder);
}
// Group examples by category
const grouped = new Map<Category, Example[]>();
for (const ex of examples) {
if (!grouped.has(ex.category)) grouped.set(ex.category, []);
grouped.get(ex.category)!.push(ex);
}
// Optional: sort titles within each group
for (const [cat, list] of grouped) {
// list.sort((a, b) => a.title.localeCompare(b.title));
grouped.set(cat, list);
}
// Create optgroups in your preferred order (and then any extras)
const categoriesToRender: Category[] = [
...CATEGORY_ORDER.filter((c) => grouped.has(c)),
...Array.from(grouped.keys()).filter((c) => !CATEGORY_ORDER.includes(c))
.sort(),
];
// We'll store a stable reference via an index into the examples array
// (simplest + avoids encoding large machine strings into <option value>)
const indexByIdentity = new Map<Example, number>();
examples.forEach((ex, i) => indexByIdentity.set(ex, i));
for (const category of categoriesToRender) {
const optgroup = document.createElement("optgroup");
optgroup.label = category;
for (const ex of grouped.get(category)!) {
const opt = document.createElement("option");
opt.value = String(indexByIdentity.get(ex)!); // index
opt.textContent = ex.title;
optgroup.appendChild(opt);
}
selectEl.appendChild(optgroup);
}
// Change handler
selectEl.onchange = () => {
const v = selectEl.value;
if (!v) return;
const picked = examples[Number(v)];
if (picked && onPick) onPick(picked);
selectEl.value = "";
};
}
const selectEl = document.getElementById("exampleSelect") as HTMLSelectElement;
buildExamplesDropdown(selectEl, examples, (example) => {
bus.emit("example/selected", example);
});