Principle:Spcl Graph of thoughts Graph Reasoning Execution
| Knowledge Sources | |
|---|---|
| Domains | Graph_Reasoning, LLM_Orchestration |
| Last Updated | 2026-02-14 12:00 GMT |
Overview
Execution model that traverses a directed acyclic graph of thought operations, executing each operation when all predecessors are complete, to produce a Graph Reasoning State.
Description
The Graph Reasoning Execution principle defines how the Controller orchestrates the execution of a Graph of Operations (GoO). The Controller drives all reasoning by walking the GoO in breadth-first order, ensuring that every operation runs only after all of its data dependencies have been satisfied.
The execution proceeds as follows:
- The Controller inspects the GoO and identifies all root operations -- those with no predecessors. These are placed into an execution queue.
- The Controller pops the first operation from the queue and executes it. Execution means invoking the operation with four key collaborators: the language model (LM), the Prompter (which generates prompts from thought state), the Parser (which interprets LLM responses into thought state), and the problem parameters dict (which carries initial and contextual data).
- After the operation completes, the Controller examines each of the operation's successors. For each successor, it checks whether all of that successor's predecessors have now been executed. If so, the successor is appended to the execution queue.
- This process repeats until the queue is empty, at which point every reachable operation in the GoO has been executed.
The result of this execution is a fully populated Graph Reasoning State (GRS): every operation's output thoughts contain the LLM-generated content, scores, validation flags, and ground truth comparisons that were produced during execution. The leaf operations' thoughts represent the final reasoning outputs.
Usage
Use this principle when you need to execute a multi-step reasoning process over a large language model, where individual reasoning steps have data dependencies that form a directed acyclic graph. This is the core execution paradigm of Graph of Thoughts. It applies whenever:
- You have decomposed a problem into multiple LLM calls with defined ordering constraints
- Some reasoning steps depend on the outputs of earlier steps
- You want parallel branches of reasoning that converge at aggregation points
- You need a deterministic, reproducible execution order for graph-structured LLM workflows
This principle subsumes simpler patterns: a single operation (IO), a linear chain (CoT), and a tree with selection (ToT) are all special cases of DAG execution.
Theoretical Basis
BFS Topological Traversal of a DAG
The execution model is a breadth-first topological traversal of a directed acyclic graph. In this formulation:
- Nodes are operations (Generate, Score, Aggregate, KeepBestN, etc.)
- Edges represent data flow dependencies (predecessor -> successor)
- Roots are entry points with no predecessors (in-degree zero)
- Leaves are exit points with no successors (out-degree zero)
An operation can execute if and only if all of its predecessors have already been executed. This is the standard topological ordering constraint, enforced dynamically via a BFS queue rather than a pre-computed static ordering.
Pseudocode:
queue = [op for op in graph.operations if op.can_be_executed()]
while queue:
op = queue.pop(0)
op.execute(lm, prompter, parser, **problem_params)
for successor in op.successors:
if successor.can_be_executed():
queue.append(successor)
Properties of this traversal:
- Correctness: Every operation executes only after all predecessors, so data dependencies are always satisfied.
- Completeness: Every reachable operation in the DAG will eventually execute, assuming the graph is connected from at least one root.
- Determinism: Given a fixed graph topology and fixed LLM responses, the execution order is deterministic (BFS level-order among independent operations).
- Termination: The DAG has no cycles, so the queue is guaranteed to drain.
The BFS approach naturally handles fan-out (one operation with multiple successors), fan-in (one operation with multiple predecessors), and diamond patterns (fan-out followed by fan-in), which are the topologies that distinguish GoT from simpler paradigms like CoT and ToT.