Prior-Art Survey: Method and Ledger

This page documents how the prior-art survey behind the comparison guide, the statement of need, and the JOSS paper’s “State of the field” section was carried out, so that the survey’s central claim is reproducible and datable rather than an assertion.

Survey date: 26 July 2026.

Claim supported. As of the survey date, no located package combines BooFun’s three-part focus — Fourier-analytic Boolean-function measures, property testing, and query complexity — in one library. CircuitGraph is the clearest published partial overlap (influence and average sensitivity via model counting); fbool is the closest unpublished one (Fourier metrics, influence, sensitivity, certificate complexity). This is a scoped, dated search result, not proof of absence.

Method

The survey ran keyword searches against the sources below, then verified every candidate against primary sources before classifying it.

Sources and query strings

Source	Queries run
JOSS paper search (`joss.theoj.org`)	`Boolean function`, `Boolean network`, `S-box`, `binary decision diagram`, `property testing`, `query complexity`, `Walsh`, `Fourier analysis`
Crossref REST API (`api.crossref.org/works`)	bibliographic queries for each candidate’s title/authors, and direct DOI record fetches to verify venue, year, authors, and title of every citation used
PyPI (`pypi.org/search`)	`boolean function`, `walsh hadamard`, `boolean fourier`, `s-box`, `property testing`, `canalization`
CRAN (incl. archive)	`boolean`, `boolfun`; archive status checked at `cran.r-project.org/src/contrib/Archive/`
crates.io	`boolean function`, `walsh`
GitHub search	`boolean function analysis`, `boolean function library`, `walsh spectrum`, topic `boolean-functions`; plus direct lookups of every named candidate
Julia registry (`juliapackages.com`)	`walsh`, `hadamard`, `boolean`
General web search (dated engine results)	`Python package "analysis of Boolean functions" Fourier influence noise stability library`, `Julia package Boolean functions Walsh Hadamard influence sensitivity`, `cryptographic Boolean functions MATLAB toolbox nonlinearity Walsh spectrum algebraic immunity`, `property testing library junta monotonicity software implementation`, `software hypercontractivity noise operator Boolean cube implementation`, `Banzhaf Shapley power index Python library`, `py-aiger-spectral Boolan Fourier boolean functions`, `JOSS Boolean function property testing package 2022..2026`

Verification protocol

For each candidate surfaced by any query:

Locate the primary artifact (repository and/or package registry entry).
If a paper is claimed, verify its metadata (venue, year, DOI, authors) through Crossref or the publisher — not through secondary mentions.
Establish capabilities from the project’s documented public API (API reference, README examples), not from abstracts or taglines.
Record maintenance status (last release/commit, archived flags).

Inclusion criteria

A system enters the comparison documents if it computes function-level analytic quantities of Boolean functions (spectra, influence, sensitivity, complexity measures, testing, cryptographic criteria) through a public API. Systems are classified as: direct overlap (shares part of BooFun’s Fourier/testing/complexity core), specialized cryptographic, networks/biology, BDD/circuits/synthesis, transform kernels (fast transforms without function-analysis semantics), or out of scope.

Candidate ledger

Every system evaluated, including rejections — so a future re-run can diff against this list.

Direct or materially overlapping

System	Evidence checked	Notes
boolfun (R)	R Journal 2011, DOI; CRAN archive	Peer-reviewed scalar crypto predecessor; archived 2012
VBF (C++)	ACM TOMS 2016, DOI; manual	Peer-reviewed vectorial crypto predecessor
fbool (Rust + Python)	GitHub README/API, PyPI, v0.2.0 tag	Closest modern Fourier-analytic neighbor; not peer reviewed
py-aiger-spectral	GitHub README	Fourier coefficients/degree weights over AIGs; no release or paper
Boolan	GitHub README	Small unmaintained package: influences, degree weights, variance, noise sensitivity
CircuitGraph	JOSS 2020, DOI; API docs	Influence + average sensitivity via model counting
QuantumQueryOptimizer	ESA 2023, DOI	Exact general-adversary SDP; used as a pinned cross-validation reference for BooFun’s certified adversary lower bounds
Aaronson’s Boolean Function Wizard	paper (2000)	Historical query-complexity lineage; unmaintained
Avishay Tal’s scripts	course materials	Reference implementations, not a versioned package

Specialized cryptographic

System	Evidence checked	Notes
SageMath `sage.crypto.boolean_function`	Sage reference docs	Walsh spectrum, nonlinearity, algebraic immunity; used as a pinned fixture reference
sboxU	GitHub	Sage/C++ S-box cryptanalysis; APN, equivalence
BooLSPLG	Mathematics 2023, DOI	Peer-reviewed CUDA C/C++ GPU library; Walsh/autocorrelation spectra, nonlinearity, degree, LAT/DDT, n ≤ 20
BoolCrypt	GitHub; ePrint 2022/428	Sage-based vectorial functions; affine/CCZ equivalence via SAT
PEIGEN	IACR ToSC 2019	S-box evaluation/implementation/generation platform
BSbox-tools	project page	Menu-driven predecessor from the BooLSPLG group; subsumed by BooLSPLG here
`boolean_function` (Rust crate)	crates.io, docs.rs	Crypto properties in Rust; cross-validation candidate (#116)
boolbox	GitHub	ANF/Möbius + quantum-circuit synthesis; pre-release, not on PyPI — below maturity threshold

Boolean networks / systems biology

BoolForge (arXiv:2509.02496; live cross-validation reference), CANA (Frontiers in Physiology 2018; Bioinformatics 2025), pyboolnet, biobalm, PyDrugLogics, emba, NORDic. Network-level dynamics; function-level activities/sensitivity overlap only.

BDD / circuits / synthesis

pyeda, Biddy (JOSS 2019), sboxgates (JOSS 2021), CUDD, ABC, espresso. Representation and synthesis, not spectral analysis.

Transform kernels (no function-analysis semantics)

System	Notes
pyfwht / libfwht	CPU/OpenMP/CUDA fast Walsh–Hadamard transforms; an optional BooFun dependency, not a competing analysis library
Hadamard.jl (absorbed Walsh.jl)	Julia FWHT kernels
SymPy `fwht`	Transform function only
SPbLA	Sparse linear algebra over the Boolean semiring; terminological, not functional, overlap

Out of scope / adjacent domains

Power-index packages (powerindex, powerindices, tucoopy, CooperativeGames, power-bdd): Banzhaf/Shapley–Shubik for weighted voting games via dynamic programming or BDDs. No Fourier machinery; adjacent only through the influence ↔ Banzhaf correspondence.
Boolin.jl: small helpers mirroring Mathematica’s BooleanFunction.
Mathematica (BooleanFunction, BooleanConvert, BooleanMinimize): symbolic manipulation and minimization; no documented spectral/influence analysis.
MATLAB: no located dedicated Boolean-function analysis toolbox (fwht transform only).

Limitations and how to re-run

The survey is limited to English-language, indexed sources on the survey date; capability judgments rest on documented public APIs, and undocumented features would be missed. To update it: re-run the queries in the table above, diff new candidates against the ledger, verify any additions via the protocol, and bump the survey date everywhere it appears (this page, the comparison guide, the statement of need, and the paper).