Can Transformers Reason Logically? A Study in SAT Solving

Leyan Pan, Vijay Ganesh, Jacob Abernethy, Chris Esposo, Wenke Lee

Keywords: Transformer LLMs, Logical Reasoning, Chain-of-Thought, SAT Solving, Backtracking

TL;DR: The Transformer architecture can perform Boolean Reasoning

Abstract:

We theoretically and empirically study the logical reasoning capabilities of LLMs in the context of the Boolean satisfiability (SAT) problem.
First, we construct a non-uniform class of decoder-only Transformers that can solve 3-SAT using backtracking and deduction via Chain-of-Thought (CoT). We prove its correctness by showing trace equivalence to the well-known DPLL SAT-solving algorithm. Second, to support the implementation of this abstract construction, we design a compiler PARAT that takes a procedural specification as input and outputs a transformer model to implement this specification. Third, rather than programming a transformer to reason, we evaluate empirically whether it can be trained to do so by learning directly from algorithmic traces (``reasoning paths'') of the DPLL algorithm.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 11011