{"paper":{"title":"On the Complexity of Checking Soundness of Natural Reductions (Extended Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Deciding whether a natural reduction is sound with respect to a commutativity relation is coNP-hard even for locking synchronization.","cross_cats":[],"primary_cat":"cs.PL","authors_text":"Azadeh Farzan, Constantin Enea, Dominik Klumpp","submitted_at":"2026-05-13T17:01:51Z","abstract_excerpt":"The verification of reductions, representative subsets of interleavings, simplifies correctness proofs of parameterized concurrent programs. We introduce an expressive class of syntactic reductions, which we call natural reductions. Natural reductions are specified by introducing atomic blocks and global rendezvous points in the parameterized program's thread template. We study the problem of deciding whether a given natural reduction is sound wrt. a given (semi-)commutativity relation. In the case that there is no synchronization between threads, we present a sound and complete polynomial-tim"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The problem of deciding whether a given natural reduction is sound with respect to a given (semi-)commutativity relation is coNP-hard already for a simple synchronization mechanism like locking.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reductions are purely syntactic (atomic blocks and global rendezvous points inserted into the thread template) and the commutativity relation is given as input; if real programs require more complex or data-dependent synchronization, the hardness result may not directly apply.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Natural reductions for concurrent programs admit a sound-and-complete polynomial-time soundness check without synchronization but are coNP-hard under locking.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Deciding whether a natural reduction is sound with respect to a commutativity relation is coNP-hard even for locking synchronization.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"64ef6fd0785c5603cd228485720a6cbea247e2ae4b9923812bcf058e83bd00c7"},"source":{"id":"2605.13780","kind":"arxiv","version":1},"verdict":{"id":"443037c8-b26b-4f5a-84b6-459f6d24bb61","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:25:38.251357Z","strongest_claim":"The problem of deciding whether a given natural reduction is sound with respect to a given (semi-)commutativity relation is coNP-hard already for a simple synchronization mechanism like locking.","one_line_summary":"Natural reductions for concurrent programs admit a sound-and-complete polynomial-time soundness check without synchronization but are coNP-hard under locking.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reductions are purely syntactic (atomic blocks and global rendezvous points inserted into the thread template) and the commutativity relation is given as input; if real programs require more complex or data-dependent synchronization, the hardness result may not directly apply.","pith_extraction_headline":"Deciding whether a natural reduction is sound with respect to a commutativity relation is coNP-hard even for locking synchronization."},"references":{"count":20,"sample":[{"doi":"10.1007/978-3-642-37036-6_17","year":2013,"title":"Bouajjani, A., Emmi, M., Enea, C., Hamza, J.: Verifying concurrent programs against sequential specifications. 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ACM (1988). https://doi.org/10. 1145/62546.62556","work_id":"52daf280-bdc6-4e26-bbec-805b83a4898c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1142/9789814261456_","year":1995,"title":"In: The Book of Traces, pp","work_id":"562f5631-d373-479f-957f-12eea52e3176","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-3-030-25543-5_20","year":2019,"title":"Damian, A., Dragoi, C., Militaru, A., Widder, J.: Communication-closed asyn- chronous protocols. In: CAV (2). pp. 344–363. Lecture Notes in Computer Science, Springer (2019). https://doi.org/10.1007/9","work_id":"582b6961-d7b6-45d9-b330-28cd280d6186","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":20,"snapshot_sha256":"69cd6542427fc234ce15b7a8b8c475ab1ca7d5613b9d76c9d0a8e02f88328dde","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}