{"paper":{"title":"Fixed Parameter Tractable Linearizability Monitoring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Linearizability monitoring for stacks, queues, and maps is fixed-parameter tractable in the number of processes.","cross_cats":["cs.CC"],"primary_cat":"cs.PL","authors_text":"Lee Zheng Han, Umang Mathur","submitted_at":"2025-09-06T04:18:43Z","abstract_excerpt":"We study the linearizability monitoring problem, which asks whether a given concurrent history of a data structure is equivalent to some sequential execution of the same data structure. In general, this problem is $\\textsf{NP}$-hard, even for simple objects such as registers. Recent work has identified tractable cases for restricted classes of histories, notably unambiguous and differentiated histories.\n  We revisit the tractability boundary from a fine-grained, parameterized perspective. We show that for a broad class of data structures -- including stacks, queues, priority queues, and maps -"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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)).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Linearizability monitoring for stacks, queues, and maps is fixed-parameter tractable in the number of processes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1ef69e8fde7e602dbe3502a65c41095b3f485bf1bd77891783a90c8d551b4eea"},"source":{"id":"2509.05586","kind":"arxiv","version":4},"verdict":{"id":"62acc288-81c9-43f5-aa7c-52ab94293e11","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T18:52:31.559968Z","strongest_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)).","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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).","pith_extraction_headline":"Linearizability monitoring for stacks, queues, and maps is fixed-parameter tractable in the number of processes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.05586/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"675989aca46bd5ac139b84829a94b5d8502a17bdfce54b7c236428c6a1d34e48"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}