File size: 3,335 Bytes
1cdfc83 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | // Application 1: Combinatorial Fault Isolation
// Assign DSS weights to test factors. When a test fails, the aggregate
// signal (sum of active factor weights) reveals the interaction ORDER
// (2-way, 3-way, etc.) without enumerating all subsets.
import { computeGreedySequence, isDSS, cardinalityFromSum, buildCardinalityTable } from './greedy.mjs';
export function runFaultIsolationDemo() {
console.log('='.repeat(70));
console.log(' FAULT ISOLATION via DSS WEIGHTS');
console.log(' Erdos-Straus Greedy Sequence Application');
console.log('='.repeat(70));
console.log();
const NUM_FACTORS = 12;
const weights = computeGreedySequence(NUM_FACTORS);
console.log(`Test system with ${NUM_FACTORS} factors.`);
console.log(`DSS weights assigned: [${weights.join(', ')}]`);
console.log(`Max weight: ${weights[weights.length - 1]} (fits in ${Math.ceil(Math.log2(weights[weights.length - 1] + 1))} bits)`);
console.log();
const factorNames = [
'Auth', 'Database', 'Cache', 'Network', 'FileIO', 'Scheduler',
'Parser', 'Serializer', 'Logger', 'Config', 'Metrics', 'Queue'
];
// Simulate failing test scenarios
const scenarios = [
{ name: '2-way interaction', factors: [1, 4] }, // Database + Network
{ name: '3-way interaction', factors: [0, 2, 5] }, // Auth + Cache + Scheduler
{ name: '4-way interaction', factors: [3, 6, 7, 9] }, // Network + Parser + Serializer + Config
{ name: '1-way (single fault)', factors: [8] }, // Logger alone
{ name: '5-way interaction', factors: [0, 1, 3, 7, 11] },
];
const table = buildCardinalityTable(weights);
console.log('SCENARIO ANALYSIS:');
console.log('-'.repeat(70));
for (const scenario of scenarios) {
const activeWeights = scenario.factors.map(i => weights[i]);
const observedSum = activeWeights.reduce((a, b) => a + b, 0);
const detectedCardinality = table.get(observedSum);
const activeNames = scenario.factors.map(i => factorNames[i]);
console.log(`\n Scenario: ${scenario.name}`);
console.log(` Active factors: [${activeNames.join(', ')}]`);
console.log(` Weights: [${activeWeights.join(' + ')}] = ${observedSum}`);
console.log(` DSS Oracle says: "${detectedCardinality}-way interaction"`);
console.log(` Correct: ${detectedCardinality === scenario.factors.length ? 'YES' : 'NO'}`);
// Show the search space reduction
const totalSubsets = (1 << NUM_FACTORS) - 1;
const subsetsOfSameCard = comb(NUM_FACTORS, detectedCardinality);
const reduction = ((1 - subsetsOfSameCard / totalSubsets) * 100).toFixed(1);
console.log(` Search space: ${totalSubsets} subsets -> ${subsetsOfSameCard} (${reduction}% reduction)`);
}
console.log('\n' + '-'.repeat(70));
console.log('\nKEY INSIGHT: From a SINGLE aggregate number, the DSS property');
console.log('reveals the interaction order. No enumeration needed.');
console.log('Traditional fault isolation: O(2^n). With DSS oracle: O(C(n,k)).');
console.log();
return { weights, scenarios, table };
}
function comb(n, k) {
if (k > n) return 0;
if (k === 0 || k === n) return 1;
let result = 1;
for (let i = 0; i < k; i++) {
result = result * (n - i) / (i + 1);
}
return Math.round(result);
}
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