基于神经网络的3-SAT求解：子句表示的输入转换方案问询

Hey there! Let's work through how to translate your SATLIB 3-SAT clause format into a neural network input (specifically for Neuroph) and nail down the input node configuration, plus map out the output setup for your "is this formula satisfiable?" question.

You mentioned the rules: 0 marks the end of a clause, 1-3 (I assume this is a simplified example—SATLIB datasets usually have more variables) are variable IDs, and - denotes negation. For example, a clause like -1 2 -3 0 translates to the logical statement: ¬x₁ ∨ x₂ ∨ ¬x₃ (not x1 OR x2 OR not x3). That's our starting point.

Neural networks need numerical inputs, so we have two practical ways to encode your clauses and variables. Let's break them down based on your end goal:

Option 1: Encode the Entire Formula (For "Is This Formula Satisfiable?" Output) #

If your network’s job is to take an entire 3-SAT formula (all clauses) and output whether any valid variable assignment exists to satisfy it, this is the right approach.

How to Encode: #

Assume your SATLIB dataset has formulas with a fixed number of clauses (m) and variables (n)—most standard 3-SAT datasets (like uf20-91) follow this.

• For each of the 3 literals in every clause, assign one input node:
  • Set the node to 1 if the literal is a positive variable (e.g., 2 → x₂ is positive)
  • Set the node to -1 if the literal is a negated variable (e.g., -3 → ¬x₃)
  • Ignore the 0 clause terminator entirely—we don’t need it in the input.
• Input Node Count: 3 * m (3 literals per clause × total clauses). For example, 91 clauses would mean 273 input nodes.

Example: #

Take a formula with 2 clauses: -1 2 -3 0 and 1 -2 3 0
Your input vector would be: [-1, 1, -1, 1, -1, 1]

Option 2: Encode Variable Assignments (For "Does This Assignment Satisfy the Formula?" Output) #

If you want the network to check if a specific variable assignment works for a formula, use this simpler encoding.

• Each variable gets one input node:
  • Set the node to 1 if the variable is assigned true
  • Set the node to 0 if the variable is assigned false
• Input Node Count: Equal to the total number of variables n in your dataset.

Note: #

To answer the broader "is the formula satisfiable?" question with this setup, you’d need to pair the network with a search algorithm (like backtracking) to test assignments—but this is less common for direct classification of formulas.

Since your goal is a yes/no answer ("satisfiable" or not), keep it simple:

• Output Node Count: 1 single node
• Activation Function: Use a Sigmoid function (Neuroph supports this out of the box)
  • Output values ≥ 0.5 mean the formula is satisfiable
  • Output values < 0.5 mean the formula is unsatisfiable

• Preprocess Your Data First: Convert every SATLIB clause file into the numerical input vectors we discussed. For labeled datasets (like uf = satisfiable, uuf = unsatisfiable), pair each input vector with a label (1 for satisfiable, 0 for unsatisfiable).
• Build the Network: Use Neuroph’s MultiLayerPerceptron class. For example, with 273 input nodes, try a hidden layer setup like 128 → 64 nodes, then 1 output node.
• Training: Use backpropagation (Neuroph’s default trainer works here) with your labeled dataset.

That should clear up how to map your clause format to neural network inputs and set up the nodes correctly!

内容的提问来源于stack exchange，提问作者Morticia A. Addams