computer-science-processes-database/processes/theory/theory-computational-complexity-analysis.json

{
  "id": "theory-computational-complexity-analysis",
  "name": "Computational Complexity Analysis",
  "category": "computer_science",
  "subcategory": "theory",
  "subcategory_name": "Theoretical Computer Science",
  "description": "Computational Complexity Analysis process visualization. This process flowchart outlines key steps, checks, and outputs.",
  "complexity": {
    "nodes": 10,
    "edges": 10,
    "conditionals": 1,
    "logicGates": {
      "orGates": 1,
      "andGates": 1,
      "notGates": 0,
      "total": 2
    },
    "level": "high",
    "detailLevel": "source_grounded_rebuild",
    "loops": 1
  },
  "colorScheme": {
    "red": {
      "hex": "#ff6b6b",
      "category": "Triggers & Inputs"
    },
    "yellow": {
      "hex": "#ffd43b",
      "category": "Structures & Objects"
    },
    "green": {
      "hex": "#51cf66",
      "category": "Processing & Operations"
    },
    "blue": {
      "hex": "#74c0fc",
      "category": "Intermediates & States"
    },
    "violet": {
      "hex": "#b197fc",
      "category": "Products & Outputs"
    }
  },
  "mermaid": "graph TD\n    N1[\"Computational Complexity...\"]\n    N2[\"Algorithm\"]\n    N3[\"Input Size n\"]\n    N4[\"Cost Model\"]\n    N5[\"Dominant Ops\"]\n    N6[\"Count Steps\"]\n    N7[\"Solve Asymptotics\"]\n    N8[\"Big-O Bound\"]\n    N9{\"Source-grounded check...\"}\n    N10[\"Computational Complexity...\"]\n\n    N1 --> N2\n    N2 --> N3\n    N3 --> N4\n    N4 --> N5\n    N5 --> N6\n    N6 --> N7\n    N7 --> N8\n    N8 --> N9\n    N9 -->|yes| N10\n    N8 -->|iterate| N3\n\n    style N1 fill:#ff6b6b,color:#fff\n    style N2 fill:#ff6b6b,color:#fff\n    style N3 fill:#ff6b6b,color:#fff\n    style N4 fill:#ffd43b,color:#000\n    style N5 fill:#ffd43b,color:#000\n    style N6 fill:#51cf66,color:#fff\n    style N7 fill:#51cf66,color:#fff\n    style N8 fill:#b197fc,color:#fff\n    style N9 fill:#ffd43b,color:#000\n    style N10 fill:#b197fc,color:#fff",
  "sources": [
    {
      "title": "Introduction to the Theory of Computation",
      "authors": "Sipser, M.",
      "journal": "Cengage",
      "year": "2012",
      "pubmed": null,
      "doi": null,
      "url": "https://www.cengage.com/c/introduction-to-the-theory-of-computation-3e-sipser/"
    },
    {
      "title": "Computational Complexity",
      "authors": "Papadimitriou, C. H.",
      "journal": "Addison-Wesley",
      "year": "1994",
      "pubmed": null,
      "doi": null,
      "url": "https://dl.acm.org/doi/book/10.5555/530612"
    },
    {
      "title": "Types and Programming Languages",
      "authors": "Pierce, B. C.",
      "journal": "MIT Press",
      "year": "2002",
      "pubmed": null,
      "doi": null,
      "url": "https://mitpress.mit.edu/9780262162098/types-and-programming-languages/"
    }
  ],
  "keywords": [
    "computational",
    "complexity",
    "analysis"
  ],
  "relatedProcesses": [],
  "created": "2026-01-15",
  "lastUpdated": "2026-04-30",
  "verified": false,
  "notes": "Corrective rebuild: replaces the generic scaffold with a process-specific step structure and records topology for duplicate detection.",
  "namedCollections": [],
  "graphMetrics": {
    "nodes": 10,
    "edges": 10,
    "conditionals": 1,
    "andGates": 1,
    "orGates": 1,
    "notGates": 0,
    "loops": 1
  },
  "nodeDetails": [
    {
      "id": "N1",
      "label": "Computational Complexity...",
      "detail": "Computational Complexity Analysis research question",
      "type": "process",
      "role": "Triggers & Inputs"
    },
    {
      "id": "N2",
      "label": "Algorithm",
      "detail": "Algorithm",
      "type": "process",
      "role": "Triggers & Inputs"
    },
    {
      "id": "N3",
      "label": "Input Size n",
      "detail": "Input Size n",
      "type": "process",
      "role": "Triggers & Inputs"
    },
    {
      "id": "N4",
      "label": "Cost Model",
      "detail": "Cost Model",
      "type": "process",
      "role": "Structures & Objects"
    },
    {
      "id": "N5",
      "label": "Dominant Ops",
      "detail": "Dominant Ops",
      "type": "process",
      "role": "Structures & Objects"
    },
    {
      "id": "N6",
      "label": "Count Steps",
      "detail": "Count Steps",
      "type": "process",
      "role": "Processing & Operations"
    },
    {
      "id": "N7",
      "label": "Solve Asymptotics",
      "detail": "Solve Asymptotics",
      "type": "process",
      "role": "Processing & Operations"
    },
    {
      "id": "N8",
      "label": "Big-O Bound",
      "detail": "Big-O Bound",
      "type": "process",
      "role": "Products & Outputs"
    },
    {
      "id": "N9",
      "label": "Source-grounded check...",
      "detail": "Source-grounded check: Introduction to the Theory of Computation",
      "type": "decision",
      "role": "Structures & Objects"
    },
    {
      "id": "N10",
      "label": "Computational Complexity...",
      "detail": "Computational Complexity Analysis prediction/readout",
      "type": "process",
      "role": "Products & Outputs"
    }
  ],
  "flowchartStandard": {
    "name": "source_grounded_rebuild_v1",
    "applied": "2026-04-30",
    "curationStatus": "source_grounded_draft",
    "basis": "cs_exact_template",
    "topologySignature": "81609272fb7f193b",
    "sourceGrounding": "Graph steps are derived from the process title, existing source metadata, and curated process/subfield templates; citations support the process topic and should be reviewed for node-level claims before marking verified."
  }
}