Pith Number

pith:JLWBN7CF

pith:2026:JLWBN7CF5OFCISJJCWRCBORCYG

not attested not anchored not stored refs resolved

The Complexity of Nested Reset Counter Systems

A. R. Balasubramanian, Franzisco Schmidt

Coverability for nested reset counter systems over order-k counters is F_Ωk-complete.

arxiv:2605.14850 v1 · 2026-05-14 · cs.FL · cs.CC · cs.LO

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\usepackage{pith}
\pithnumber{JLWBN7CF5OFCISJJCWRCBORCYG}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that coverability for NRCS over order-k counters is F_Ωk-complete where Ωk is the tower of height k of the ω ordinal.

C2weakest assumption

The chosen semantics for resets on higher-order counters does not introduce hidden complexity beyond the ordinal tower construction used in the length-function theorems.

C3one line summary

Coverability for order-k nested reset counter systems is F_Ωk-complete.

References

48 extracted · 48 resolved · 2 Pith anchors

[1] 2016 , url = 2016 · doi:10.1145/2858784

[2] Normann Decker and Daniel Thoma , editor =. On Freeze. Foundations of Software Science and Computation Structures - 19th International Conference,. 2016 , url =. doi:10.1007/978-3-662-49630-5\_16 , ti 2016 · doi:10.1007/978-3-662-49630-5

[3] On Freeze LTL with Ordered Attributes 2015 · arXiv:1504.06355

[4] Lomazova and Philippe Schnoebelen , editor = 1999 · doi:10.1007/3-540-46562-6

[6] Revisiting Ackermann-Hardness for Lossy Counter Machines and Reset Petri Nets , booktitle = 2010 · doi:10.1007/978-3-642-15155-2

Receipt and verification

First computed	2026-05-17T23:38:56.335035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4aec16fc45eb8a24492915a220ba22c18b65555cb3d1f4d390f78af05c87ee29

Aliases

arxiv: 2605.14850 · arxiv_version: 2605.14850v1 · doi: 10.48550/arxiv.2605.14850 · pith_short_12: JLWBN7CF5OFC · pith_short_16: JLWBN7CF5OFCISJJ · pith_short_8: JLWBN7CF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JLWBN7CF5OFCISJJCWRCBORCYG \
  | 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: 4aec16fc45eb8a24492915a220ba22c18b65555cb3d1f4d390f78af05c87ee29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec52033aacdf07608db37d04da4ac6e2fc88101dc679ebcbc655cf735518ab19",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2026-05-14T13:58:33Z",
    "title_canon_sha256": "fede70b72cdbb1b15b7474d8e4e84b9068decf0c35e5c31ac25484849d60fbae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14850",
    "kind": "arxiv",
    "version": 1
  }
}