What is the primary purpose of the Three-Match skill?

It reduces 3-SAT boolean satisfiability problems into colored subgraph isomorphism problems using specialized topological gadgets for more efficient or specialized solving.

How does Möbius filtering benefit the logic resolution?

Möbius inversion is used as a bidirectional filter to cancel out backtracking and composite paths, ensuring the algorithm only processes prime, non-revisiting geodesics.

What does 'correct by construction' mean in this context?

It implies that the local constraints of the 3-MATCH gadgets are designed such that any valid local configuration mathematically guarantees a global solution to the original 3-SAT problem.

Does this skill require specific mathematical knowledge?

While the skill automates the process, it is based on GF(3) conservation, 3-adic valuations, and Ramanujan properties, which are common in advanced graph theory and cryptography.

Three-Match SAT Resolver

Name: Three-Match SAT Resolver
Author: plurigrid

byplurigrid

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Data Science & ML

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

About

Three-Match is a specialized computational logic skill that leverages topological constraints and graph theory to solve complex 3-SAT problems. By transforming 3-SAT clauses into colored subgraph isomorphism tasks, it ensures global correctness through local constraint enforcement using GF(3) conservation and 3-adic valuation. This skill is particularly useful for developers and researchers working in formal verification, logic optimization, and topological computing, providing a 'correct by construction' framework that filters out backtracking using Möbius inversion and prime path geodesics.

Key Features

Provides verified gadgets for mapping individual 3-SAT clauses to graph structures
Reduces 3-SAT complexity to 3-coloring and colored subgraph isomorphism
Implements non-backtracking geodesics (prime paths) to prevent state revisitation
Enforces local constraints via GF(3) conservation and 3-adic valuation
Applies Möbius inversion filtering to maintain path integrity and high spectral gaps
2 GitHub stars

Use Cases

Formal verification of complex logic circuits and constraint satisfaction problems
Solving Boolean satisfiability through advanced mathematical and algebraic geometry methods
Graph-based algorithmic research and topological computational modeling

About

Key Features

Provides verified gadgets for mapping individual 3-SAT clauses to graph structures
Reduces 3-SAT complexity to 3-coloring and colored subgraph isomorphism
Implements non-backtracking geodesics (prime paths) to prevent state revisitation
Enforces local constraints via GF(3) conservation and 3-adic valuation
Applies Möbius inversion filtering to maintain path integrity and high spectral gaps
2 GitHub stars

Use Cases

Formal verification of complex logic circuits and constraint satisfaction problems
Solving Boolean satisfiability through advanced mathematical and algebraic geometry methods
Graph-based algorithmic research and topological computational modeling