Pith Number

pith:QZB762IO

pith:2026:QZB762IOOWXXA6SJ43OQLLIISD

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Extending QuAK with Nested Quantitative Automata

Harun Y{\i}lmaz, N. Ege Sara\c{c}, Nicolas Mazzocchi, Thomas A. Henzinger

Flattening procedures reduce nested quantitative automata to standard ones so QuAK can reuse its existing decision procedures.

arxiv:2605.12418 v2 · 2026-05-12 · cs.FL · cs.LO

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Claims

C1strongest 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.

C2weakest 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.

C3one line summary

Extends QuAK with flattening reductions from nested quantitative automata to quantitative automata, enabling analysis of unbounded quantitative properties via existing decision procedures.

Receipt and verification

First computed	2026-05-20T01:06:10.264324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8643ff690e75af707a49e6dd05ad0890c170f310189143fdf9c5d5a687b9558a

Aliases

arxiv: 2605.12418 · arxiv_version: 2605.12418v2 · doi: 10.48550/arxiv.2605.12418 · pith_short_12: QZB762IOOWXX · pith_short_16: QZB762IOOWXXA6SJ · pith_short_8: QZB762IO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QZB762IOOWXXA6SJ43OQLLIISD \
  | 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: 8643ff690e75af707a49e6dd05ad0890c170f310189143fdf9c5d5a687b9558a

Canonical record JSON

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    "abstract_canon_sha256": "1fee80a8bbc1df34b1ef1f8c82ceb3c73d627122f7ed5e081a028ba7293f54ff",
    "cross_cats_sorted": [
      "cs.LO"
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2026-05-12T17:13:39Z",
    "title_canon_sha256": "8fdcbb40070061ed2164544e3635c440c10fa47aabe7bf658d9a1d1bc532fd47"
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  "source": {
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    "kind": "arxiv",
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