What are non-backtracking geodesics in this context?

These are 'prime' paths through a color space where no state is revisited, ensured by Möbius inversion which cancels out backtracking or 'composite' paths.

How does it ensure solution correctness?

It utilizes a 'correct-by-construction' methodology where satisfying local GF(3) conservation and non-backtracking geodesic constraints mathematically guarantees a global solution.

What is GF(3) conservation?

It is a constraint where the sum of trits (values representing colors) must be equivalent to 0 modulo 3, ensuring valid local coloring matches.

Three-Match Topological SAT Solver

Name: Three-Match Topological SAT Solver
Author: plurigrid

byplurigrid

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Data Science & ML

Reduces complex 3-SAT problems to colored subgraph isomorphism using non-backtracking geodesics and Möbius filtering.

About

Three-Match is a specialized mathematical skill that implements a rigorous reduction of 3-SAT problems into 3-coloring and colored subgraph isomorphism tasks. By leveraging GF(3) conservation, prime paths, and Möbius inversion filtering, it ensures that local geodesic constraints result in global correctness by construction. This skill is ideal for developers and researchers working in complexity theory, topological computing, and advanced algorithmic optimization who require verifiable, non-backtracking solutions to NP-complete problems.

Key Features

2 GitHub stars
Provides a 'correct-by-construction' framework for global satisfiability
Reduces 3-SAT clauses to 3-coloring constraints via specialized gadgets
Ensures GF(3) conservation (sum ≡ 0 mod 3) for verifiable local constraints
Implements non-backtracking geodesics to ensure unique state paths
Uses Möbius inversion filtering to eliminate backtracking in sequence generation

Use Cases

Implementing topological constraints in algorithmic design and chemputer simulations
Solving Boolean satisfiability (3-SAT) problems through graph-based reductions
Verifying colored subgraph isomorphism properties in complex networks

About

Key Features

2 GitHub stars
Provides a 'correct-by-construction' framework for global satisfiability
Reduces 3-SAT clauses to 3-coloring constraints via specialized gadgets
Ensures GF(3) conservation (sum ≡ 0 mod 3) for verifiable local constraints
Implements non-backtracking geodesics to ensure unique state paths
Uses Möbius inversion filtering to eliminate backtracking in sequence generation

Use Cases

Implementing topological constraints in algorithmic design and chemputer simulations
Solving Boolean satisfiability (3-SAT) problems through graph-based reductions
Verifying colored subgraph isomorphism properties in complex networks