{"paper":{"title":"Extending QuAK with Nested Quantitative Automata","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Flattening procedures reduce nested quantitative automata to standard ones so QuAK can reuse its existing decision procedures.","cross_cats":["cs.LO"],"primary_cat":"cs.FL","authors_text":"Harun Y{\\i}lmaz, N. Ege Sara\\c{c}, Nicolas Mazzocchi, Thomas A. Henzinger","submitted_at":"2026-05-12T17:13:39Z","abstract_excerpt":"Quantitative automata (QAs) extend finite-state automata on infinite words with weighted transitions to specify quantitative system properties. However, their finite weight sets rule out properties like average response time, where response times can be arbitrarily large. Nested quantitative automata (NQAs) overcome this limitation: a parent automaton spawns child automata to compute unbounded values over finite infixes and aggregates them into a final result. Despite this expressiveness, NQAs have lacked practical tool support to date. We close this gap by extending the Quantitative Automata "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our core contribution is implementing a suite of flattening procedures that reduce NQAs to QAs, leveraging QuAK's existing decision procedures. These reductions preserve the answers to threshold decision problems, while allowing users to specify properties in the more expressive NQA formalism.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the implemented flattening procedures correctly preserve semantics for all supported combinations of parent aggregators (including limits and averages) and child functions (extrema, monotonic or bounded summations), and that the known decidability results for emptiness and universality apply without gaps in the tool implementation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends QuAK with flattening reductions from nested quantitative automata to quantitative automata, enabling analysis of unbounded quantitative properties via existing decision procedures.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Flattening procedures reduce nested quantitative automata to standard ones so QuAK can reuse its existing decision procedures.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bcab70a5ad974fff1d171b24dbd1048efc11c09389842603ab57a0d6b85e40df"},"source":{"id":"2605.12418","kind":"arxiv","version":2},"verdict":{"id":"0a6c3544-7273-4a41-899b-f661240405a3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T02:28:43.069884Z","strongest_claim":"Our core contribution is implementing a suite of flattening procedures that reduce NQAs to QAs, leveraging QuAK's existing decision procedures. These reductions preserve the answers to threshold decision problems, while allowing users to specify properties in the more expressive NQA formalism.","one_line_summary":"Extends QuAK with flattening reductions from nested quantitative automata to quantitative automata, enabling analysis of unbounded quantitative properties via existing decision procedures.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the implemented flattening procedures correctly preserve semantics for all supported combinations of parent aggregators (including limits and averages) and child functions (extrema, monotonic or bounded summations), and that the known decidability results for emptiness and universality apply without gaps in the tool implementation.","pith_extraction_headline":"Flattening procedures reduce nested quantitative automata to standard ones so QuAK can reuse its existing decision procedures."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.12418/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T22:21:57.855883Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T10:35:30.895349Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T08:01:18.476667Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T07:30:58.509011Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"eea541cba78bd76c2677643bc5e73a386ac565526d199c9f4ab07db69c3fb02e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}