{
  "id": "KL-FCS-054",
  "version": "1.0.0",
  "domain": "Distributed protocols",
  "kind": "protocols",
  "title": "Atomic acquisition with three processes",
  "problem": "Check mutual exclusion over all one-shot lock-acquisition interleavings.",
  "specification": {
    "processes": 3,
    "mode": "atomic",
    "state_encoding": "process PCs, lock bit, process saved-free bits; PC 0=start, 1=checked, 2=critical, 3=done",
    "atomicity": "Atomic mode tests and acquires together; split mode tests then acquires in separate steps."
  },
  "claim": {
    "mutual_exclusion": true
  },
  "witness": {
    "method": "reachable-state enumeration"
  },
  "verification_scope": "Complete reachable interleaving graph",
  "explanation": "An atomic acquisition prevents simultaneous entry. A split acquisition can let both processes remember a free lock before either marks it occupied.",
  "limitations": "This is a shared-memory mutual-exclusion model. It does not verify a network protocol, message loss, liveness, or fairness.",
  "verification_status": "mechanically-checked",
  "review_status": "awaiting-independent-review",
  "provenance": {
    "origin": "Original Kenton Labs reference instance, authored with Codex assistance on 2026-10-11.",
    "external_dataset": null,
    "model_run": null
  },
  "references": [
    "https://lamport.azurewebsites.net/tla/tutorial/session6.html"
  ],
  "license_status": "not-yet-selected",
  "dataset": {
    "family": "protocols",
    "task": "Check mutual exclusion over all one-shot lock-acquisition interleavings.",
    "input_encoding": "Structured JSON; field meanings are stated in the specification.",
    "coverage": "Complete reachable interleaving graph",
    "acceptance": [
      "Start all processes outside the critical section with a free lock.",
      "Explore every enabled interleaving to a complete reachable closure.",
      "Check the number of processes in the critical section at each state.",
      "For a failure, replay the provided schedule to the unsafe state."
    ],
    "generation": "Deterministic finite fixture; full enumeration or witness replay as stated.",
    "split_policy": "Reference corpus for exposition and reproduction; no train/test evaluation split is claimed."
  },
  "lesson": {
    "motivation": "Treat atomicity and scheduling as part of a protocol model. A small interleaving can refute a plausible safety claim.",
    "definitions": [
      {
        "term": "Atomic step",
        "definition": "An action observed as indivisible by other processes."
      },
      {
        "term": "Mutual exclusion",
        "definition": "At most one process occupies its critical section."
      },
      {
        "term": "Interleaving",
        "definition": "A sequence choosing one enabled process action at a time."
      }
    ],
    "reasoning": [
      "Start all processes outside the critical section with a free lock.",
      "Explore every enabled interleaving to a complete reachable closure.",
      "Check the number of processes in the critical section at each state.",
      "For a failure, replay the provided schedule to the unsafe state."
    ],
    "worked_example": "An atomic acquisition prevents simultaneous entry. A split acquisition can let both processes remember a free lock before either marks it occupied.",
    "complexity": "The finite state space is exponential in the number of processes; this family uses two or three one-shot processes.",
    "common_error": "Separating a lock check from acquisition allows another process to observe the same free lock.",
    "further_work": "Extend from shared-memory concurrency to bounded message queues and explicit network faults."
  },
  "related_ids": [
    "KL-FCS-052",
    "KL-FCS-053"
  ]
}