LogicDot: A Markov Rule-Based Inference Framework for Large Language Models

Abstract

The paper introduces the LogicDot ( Logic-level Decomposition of Thought ) framework – an advanced inference method based on the Markov principle (i.e., each state depends only on the previous state, without keeping the entire history) to convert complex problems into independent atomic steps. Through the decomposition and reduction process, LogicDot allows the model to focus only on the current state, optimizing computational resources and minimizing errors due to information accumulation. Data analysis shows that most problems are divided into 2 to 4 sub-questions, reflecting the average complexity level, while problems with a larger number of sub-questions account for a low proportion. These results provide a theoretical basis and direction for developing effective inference strategies, thereby improving accuracy in multi-step tasks. The paper affirms the applicability of LogicDot in building efficient and resource-saving AI systems.