# Suffix-Constrained Greedy Search Algorithms for Causal Language Models

arXiv: https://arxiv.org/abs/2603.01243 · HTML: https://mlsanity.com/paper/2603.01243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 62 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [Constrained Language Models Yield Few-Shot Semantic Parsers](https://mlsanity.com/paper/2104.08768/) (2021)
- [NeuroLogic A*esque Decoding: Constrained Text Generation with Lookahead Heuristics](https://mlsanity.com/paper/2112.08726/) (2021)
- [NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraints](https://mlsanity.com/paper/2010.12884/) (2020)
- [Preference Leakage: A Contamination Problem in LLM-as-a-judge](https://mlsanity.com/paper/2502.01534/) (2025)
- [Guided Open Vocabulary Image Captioning with Constrained Beam Search](https://mlsanity.com/paper/1612.00576/) (2016)
- [Guiding LLMs The Right Way: Fast, Non-Invasive Constrained Generation](https://mlsanity.com/paper/2403.06988/) (2024)
- [Let Me Speak Freely? A Study on the Impact of Format Restrictions on Performance of Large Language Models](https://mlsanity.com/paper/2408.02442/) (2024)
- [An Empirical Study of LLM-as-a-Judge for LLM Evaluation: Fine-tuned Judge Model is not a General Substitute for GPT-4](https://mlsanity.com/paper/2403.02839/) (2024)
- [SynCode: LLM Generation with Grammar Augmentation](https://mlsanity.com/paper/2403.01632/) (2024)
- [One Token to Fool LLM-as-a-Judge](https://mlsanity.com/paper/2507.08794/) (2025)
- [Measuring and Controlling Instruction (In)Stability in Language Model Dialogs](https://mlsanity.com/paper/2402.10962/) (2024)
- [CRANE: Reasoning with constrained LLM generation](https://mlsanity.com/paper/2502.09061/) (2025)
- [Rating Roulette: Self-Inconsistency in LLM-As-A-Judge Frameworks](https://mlsanity.com/paper/2510.27106/) (2025)
- [Adaptable Logical Control for Large Language Models](https://mlsanity.com/paper/2406.13892/) (2024)
- [JuStRank: Benchmarking LLM Judges for System Ranking](https://mlsanity.com/paper/2412.09569/) (2024)
- [Prompting or Fine-tuning? A Comparative Study of Large Language Models for Taxonomy Construction](https://mlsanity.com/paper/2309.01715/) (2023)
- [Efficient Beam Search for Large Language Models Using Trie-Based Decoding](https://mlsanity.com/paper/2502.00085/) (2025)
- [AdapTrack: Constrained Decoding without Distorting LLM's Output Intent](https://mlsanity.com/paper/2510.17376/) (2025)
- [Prompt engineering and framework: implementation to increase code reliability based guideline for LLMs](https://mlsanity.com/paper/2506.10989/) (2025)

## Abstract (arXiv)

Large language models (LLMs) are powerful tools that have found applications beyond human-machine interfaces and chatbots. Beside free-form generation, there has been an interest in constrained generation, a setting where LLMs are constrained to generate well-formed outputs with respect to the language defined by a formal grammar. Although appealing, this setting may be over restrictive for downstream applications. For example, many LLM tasks require the model to reason freely before generating its final response in a specific format. In this work, we introduce suffix-constrained generation, a constrained generation setting in which only the end of the response is constrained by a grammar, a scenario that is not supported by existing constrained generation methods. We introduce several suffix-constrained generation algorithms that are based on greedy search. We experiment on several datasets, and show that our approach allows to guarantee suffix constraints without having a negative impact on results, and even improving them in many settings.