Pith Number

pith:44YZH6MA

pith:2025:44YZH6MAHXVGYQJ2PJWGA3VGFO

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Fixed Parameter Tractable Linearizability Monitoring

Lee Zheng Han, Umang Mathur

Linearizability monitoring for stacks, queues, and maps is fixed-parameter tractable in the number of processes.

arxiv:2509.05586 v4 · 2025-09-06 · cs.PL · cs.CC

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Claims

C1strongest claim

We show that for a broad class of data structures -- including stacks, queues, priority queues, and maps -- linearizability monitoring is fixed-parameter tractable when parameterized by the number of processes. Concretely, we give an algorithm running in time O(c^k · poly(n)).

C2weakest assumption

The sequential specifications of the considered data structures can be captured by fixed languages L for which language reachability is efficiently solvable on the specific graph structures induced by concurrent histories (as stated in the reduction to language reachability).

C3one line summary

Linearizability monitoring for stacks, queues, priority queues, and maps is fixed-parameter tractable parameterized by the number of processes via reduction to language reachability on history-induced graphs.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:15.190508Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e73193f9803dea6c413a7a6c606ea62bb619e4d9b156b3f2aff8c4e06cda86ab

Aliases

arxiv: 2509.05586 · arxiv_version: 2509.05586v4 · doi: 10.48550/arxiv.2509.05586 · pith_short_12: 44YZH6MAHXVG · pith_short_16: 44YZH6MAHXVGYQJ2 · pith_short_8: 44YZH6MA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/44YZH6MAHXVGYQJ2PJWGA3VGFO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e73193f9803dea6c413a7a6c606ea62bb619e4d9b156b3f2aff8c4e06cda86ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43a70e63ab6a359bafd3233d068522dff4ed39a9e4e303b479ae9bef114c81aa",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.PL",
    "submitted_at": "2025-09-06T04:18:43Z",
    "title_canon_sha256": "cd53e8b5e56d93e1365cb7aa88531f20f46b199c7480384f29ff9704f8953a3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05586",
    "kind": "arxiv",
    "version": 4
  }
}