# Tree of Thoughts (ToT)

> Breadth-first search over LLM states and state evaluation reference.

- Skill: `j4flmao/tree-of-thoughts-tot` (Agent Skill, multi-file: 9 files)
- Install (CLI): `npx skillmds@latest add j4flmao/tree-of-thoughts-tot`
- Raw SKILL.md: https://api.skillmd.com/api/skills/j4flmao/tree-of-thoughts-tot/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: j4flmao (https://skillmd.com/u/j4flmao)
- Updated: 2026-09-21
- Page: https://skillmd.com/skills/j4flmao/tree-of-thoughts-tot

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# Tree of Thoughts (ToT) Mechanics

Tree of Thoughts (ToT) generalizes the concept of prompt engineering by framing LLM decoding as a rigorous search over a tree where nodes represent partial solutions (thoughts). This enables the LLM to perform deliberate reasoning through exploration and backtracking.

## State Space Formulation
The problem is formulated as a tuple $(S, G, E, V, \text{Search})$, where $S$ is the state space, $G$ is the generator of thoughts, $E$ is the evaluator, and $V$ is the validation criteria.

### Breadth-First Search (BFS) Implementation
In ToT BFS, we maintain a frontier of size $b$. At step $k$, we expand each of the $b$ states by generating $k$ new thoughts.

```mermaid
flowchart TD
%%{init: {"theme": "default", "flowchart": {"useMaxWidth": true}}}%%
    subgraph SearchBFSStateSearch ["BFS State Search<br><br><br>"]
        State_0[State 0] -->|"GenerateThoughts(k=3)"| T1[Thought 1]
        State_0 -->|"GenerateThoughts(k=3)"| T2[Thought 2]
    end
    subgraph EvaluationStateEvaluationLayer ["State Evaluation Layer<br><br><br>"]
        T1 -->|"Evaluate(T1)"| E1[Score: 0.9]
        T2 -->|"Evaluate(T2)"| E2[Score: 0.4]
    end
    E1 -->|"Prune()"| Next[Next Frontier]
```

## State Evaluation Mechanisms
Evaluating states involves prompting the LLM to assess the viability of a partial solution.
- **Value Prompting**: The LLM assigns a scalar score (e.g., 1-10) or classification (sure, likely, impossible).
- **Voting**: Multiple LLM instances vote on the best thought among candidates.