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arXiv · 2606.23672

Teaching LLMs String Matching, Backtracking, and Error Recovery to Deduce Bases and Truth Tables for the Combinatorially Exploding Bit Manipulation Puzzles

Prateek Agnihotri·Sanchit Jain·Prabhat Agnihotri·Aditya Prasad·Shubham Jain
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Abstract

This paper presents our algorithmic innovations for the NVIDIA Nemotron Model Reasoning Challenge, focusing on Bit Manipulation Puzzles. In this task, the objective is to discover a hidden logical rule transforming input binary strings to outputs, then apply it to unseen inputs. Large Language Models (LLMs) notoriously struggle here; traditional methods force them to simulate complex boolean logic and arithmetic, leading to hallucinations. Furthermore, the search space of bitwise operations (combinations of shifts, rotations, and logic gates) suffers from a severe combinatorial explosion. To overcome this computational intractability, we present a novel approach that abandons arithmetic logic entirely in favor of string similarity, structured search, and autonomous error recovery. Our core contributions are: 1. Bases and Truth Table Formulation: We reframe logic-gate deduction into a base-selection task, leveraging string similarity (minimal bit flips) to isolate primitive transformations ("bases") and deduce truth tables without complex arithmetic. 2. Backtracking DFS and Error Recovery: We formalize a search process that tests candidate bases, detects logical collisions across examples, and backtracks upon failure to perform robust error recovery. 3. Bit Tokenization and Interactive Reasoning SFT: We force the tokenizer to encode binary strings as individual single-bit tokens. We use dynamic masking to simulate external oracle feedback, training the model to hypothesize, self-evaluate, and backtrack natively. Evaluated on bit manipulation puzzles, our approach achieved over 96% validation accuracy. This represents the highest performance in this category. These algorithmic and training innovations ultimately earned our team the Best Fine-tuning Method and Best Data/Synthetic Data Method awards in the contest, alongside a 7th Place overall finish on leaderboard.

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Prateek Agnihotri, Sanchit Jain, Prabhat Agnihotri, Aditya Prasad, Shubham Jain. 2026-07-22. Teaching LLMs String Matching, Backtracking, and Error Recovery to Deduce Bases and Truth Tables for the Combinatorially Exploding Bit Manipulation Puzzles. https://arxiv.org/abs/2606.23672

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