BooFun

Boolean function analysis in Python.

Tools for Fourier analysis, property testing, and complexity measures of Boolean functions. Built while studying O’Donnell’s Analysis of Boolean Functions.

Contents:

• Quick Start
  • Installation
  • Creating Functions
  • Flexible Input Types
  • Evaluation
  • Analysis
  • Properties
  • Representations
  • Visualization
  • Next
• Performance Guide
  • Quick Summary
  • Optimization Tiers
  • Memory Optimization
  • Parallelization
  • Caching and Memoization
  • Benchmarks
  • Best Practices
  • Running Benchmarks
  • Docker Performance
  • Scaling Guidelines
  • Future Optimizations
• Library Comparison
  • Summary
  • What BooFun Has
  • What BooFun Lacks
  • Comparison Tables
  • When to Use What
  • Cross-Validation
  • Installation
  • Prior Art
  • References
• Cross-Validation with Sage/Mathematica
  • Overview
  • Key Functions to Validate
  • Automated Cross-Validation
  • Known Theoretical Results
  • Integration with CI
  • References

Installation

pip install boofun

Usage

import boofun as bf

# Create
xor = bf.create([0, 1, 1, 0])
maj = bf.majority(5)

# Evaluate
maj.evaluate([1, 1, 0, 0, 1])  # 1

# Analyze
maj.fourier()           # Fourier coefficients
maj.influences()        # Variable influences
maj.noise_stability(0.9)
maj.is_monotone()

Convention

O’Donnell standard: Boolean 0 → +1, Boolean 1 → −1.

This ensures f̂(∅) = E[f].

What’s Here

• Fourier: Walsh-Hadamard transform, influences, noise stability

• Property Testing: BLR, junta, monotonicity

• Query Complexity: D(f), R(f), Q(f), sensitivity, certificates

• Representations: Truth tables, ANF, BDD, circuits, Fourier expansion

Limitations

Test coverage is low (~38%). Edge cases may have bugs. If something breaks, please report it.

API Reference

boofun

BooFun: A comprehensive Boolean function analysis library.

Indices

• Index

• Module Index