Learning and Enforcing Context-Sensitive Control for LLMs

Mohammad Albinhassan; Pranava Madhyastha; Mark Law; Alessandra Russo

cs.CLApr 12, 2026

Learning and Enforcing Context-Sensitive Control for LLMs

Authors: Mohammad Albinhassan, Pranava Madhyastha, Mark Law, Alessandra Russo

Organizations: Imperial College London · City University of London · The Alan Turing Institute · ILASP Limited, UK

Abstract

Controlling the output of Large Language Models (LLMs) through context-sensitive constraints has emerged as a promising approach to overcome the limitations of Context-Free Grammars (CFGs) in guaranteeing generation validity. However, such constraints typically require manual specification -- a significant barrier demanding specialized expertise. We introduce a framework that automatically learns context-sensitive constraints from LLM interactions through a two-phase process: syntactic exploration to gather diverse outputs for constraint learning, followed by constraint exploitation to enforce these learned rules during generation. Experiments demonstrate that our method enables even small LLMs (1B parameters) to learn and generate with perfect constraint adherence, outperforming larger counterparts and state-of-the-art reasoning models. This work represents the first integration of context-sensitive grammar learning with LLM generation, eliminating manual specification while maintaining generation validity.

Figures & tables

Figure 1: Two-phase methodology for learning context-sensitive constraints. Phase 1: An LLM

p_{\theta}

samples diverse sequences using generator

g

from a CFG -masked distribution (

q_{C_{\text{\lx@glossaries@gls@link{acronym}{cfg}{{{}}{\color[rgb]{0,0,0}CFG}} }}}

). Tokens such as bc are CFG -valid but context-sensitively invalid, leading to oracle rejection (

\mathcal{V}

) and red masking in

\hat{\mathcal{C}}_{\text{\lx@glossaries@gls@link{acronym}{asg}{{{}}{\color[rgb]{0,0,0}ASG}} }}

. Valid tokens appear green, invalid tokens red. Labeled examples form dataset

E

for the ASG learner to construct

\hat{G}

. Phase 2: The LLM uses the learned ASG -constrained distribution (

q_{\hat{C}_{G_{\mathrm{ASG}}}}

), disallowing tokens that may lead to violations (red), while valid tokens remain accessible (green), ensuring all outputs satisfy the target grammar (✓). The gear in Phase 2 illustrates all constraints have been learned (100%), so nothing new is learned (note: this is for visualization purposes only).

Model	$\mathbf{G}$	Accuracy
Model	$\mathbf{G}$	$a^{n}b^{n}c^{n}$	$a^{n}b^{n}c^{m}$
GPT 4.1	-	63.3%	76.7%
o1	-	86.7%	96.7%
o3 mini	-	63.3%	86.7%
o4 mini	-	90.0%	93.3%
DeepSeek-R1	-	80.0%	86.7%

Table 1: Accuracy results for

a^{n}b^{n}c^{n}

and

a^{n}b^{n}c^{m}

with different LLMs (Model) and grammar constraints (

\mathrm{G}

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 2 — Figure 2: The learned ASG for $a^{n}b^{n}c^{n}$ using our approach. This grammar utilizes ASP constraints (in bold and surrounded by $\{\}$ ) to enforce the context-sensitive condition that all three symbol sequences maintain equal length.

Model	$\mathbf{G}$	Accuracy
Model	$\mathbf{G}$	$a^{n}b^{n}c^{n}$	$a^{n}b^{n}c^{m}$
GPT 4.1	-	63.3%	76.7%
o1	-	86.7%	96.7%
o3 mini	-	63.3%	86.7%
o4 mini	-	90.0%	93.3%
DeepSeek-R1	-	80.0%	86.7%

Appendix

Table 2: Accuracy results for

a^{n}b^{n}c^{n}

and

a^{n}b^{n}c^{m}

with different LLMs (Model), including Llama 3.2 3B and 3.1 8B, and grammar constraints (

\mathrm{G}

Panel of Figure 3 — Figure 3: Prompt template for the a n b n c n language generation task. The system instruction defines the formal language requirements, followed by example interactions demonstrating expected inputs and outputs.

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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.

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