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Paper: Large Language Model Guided Tree-of-Thought
Link: https://arxiv.org/abs/2305.08291v1
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Let me analyze the paper and extract the key information about the Large Language Model Guided Tree-of-Thought (ToT) technique:

Examples mentioned in the paper:
1. Sudoku puzzle solving: The paper implements a ToT-based Sudoku solver and evaluates it on 3x3, 4x4, and 5x5 Sudoku puzzles.

2. General mathematical theorem proving (mentioned as a potential application): The paper suggests ToT could be used for mathematical theorem proving, where a full solution would be a complete proof, and partial solutions would be subsets of the proof steps.

Essence of Large Language Model Guided Tree-of-Thought (ToT) prompting:

The ToT technique is a framework that enhances the problem-solving capabilities of large language models (LLMs) by implementing a tree-like thought process with backtracking. It augments an LLM with additional modules to enable multi-round conversations and exploration of solution spaces.

Key ideas:
1. Inspired by human problem-solving through trial and error
2. Explores solution space through a tree-like thought process
3. Allows backtracking when necessary
4. Implements a multi-round conversation between the LLM and additional modules
5. Combines "short-range reasoning" capabilities of LLMs with enhanced "long-range reasoning" through exploration and backtracking

What it does:
1. Breaks down complex problems into smaller steps
2. Generates intermediate solutions at each step
3. Checks the validity of intermediate solutions
4. Allows backtracking to explore alternative solution paths
5. Maintains a memory of the problem-solving process
6. Provides hints and guidance to the LLM through a prompter agent

Use cases:
1. Solving complex puzzles (e.g., Sudoku, potentially other NP-complete problems)
2. Mathematical theorem proving
3. Logical reasoning tasks
4. Multi-step problem-solving in various domains
5. Tasks requiring long-term planning and solution exploration

Examples of prompting with ToT:

1. Sudoku puzzle solving:
User: "Please solve this 4x4 Sudoku puzzle [[3,*,*,2],[1,*,3,*],[*,1,*,3],[4,*,*,1]] where * represents a cell to be filled"

ToT system:
a) Prompter: "For the given 4x4 Sudoku puzzle, please derive the first step to fill an empty cell. Return the step in JSON format {next_step: <next_step>}"
b) LLM responds with a partial solution
c) Checker verifies the partial solution
d) Process repeats with backtracking if necessary

2. Mathematical theorem proving:
User: "Prove that the sum of the angles in a triangle is 180 degrees"

ToT system:
a) Prompter: "Let's start proving that the sum of angles in a triangle is 180 degrees. What's the first step in this proof? Return the step in JSON format {next_step: <next_step>}"
b) LLM provides the first step of the proof
c) Checker verifies the logical correctness of the step
d) Process continues, potentially backtracking if a step leads to a dead-end

3. Complex logical reasoning:
User: "Solve the following logic puzzle: There are five houses in a row, each painted a different color. In each house lives a person of a different nationality. The five owners drink a certain beverage, smoke a certain brand of cigar, and keep a certain pet. Using the given clues, determine who owns the fish."

ToT system:
a) Prompter: "Let's approach this logic puzzle step by step. First, list out the categories we need to consider. Return the step in JSON format {next_step: <next_step>}"
b) LLM lists the categories (house color, nationality, drink, cigar brand, pet)
c) Checker verifies the completeness of the categories
d) Prompter: "Now, let's start with the first clue. How does it help us fill in our grid? Return the step in JSON format {next_step: <next_step>}"
e) Process continues, with the system exploring different possibilities and backtracking when necessary to solve the puzzle

In each of these examples, the ToT system would engage in multiple rounds of conversation with the LLM, generating partial solutions, checking their validity, and exploring different paths in the solution space until a complete solution is found or the maximum number of conversation rounds is reached.