[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83046-en":3,"doc-seo-83046-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83046,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Shortest Prompts for Texts and Behaviors in LLMs: Prompting Complexity","The paper defines prompting complexity for fixed instruction-tuned language models: the shortest plausible human-readable prompt that makes deterministic decoding produce a target text. The measure is a model-relative analogue of resource-bounded Kolmogorov complexity, with no model-independent invariance. In finite-context settings it is enumerable, while soft prompting complexity extends it to approximate outputs. The work further introduces prompting distance and behavioral prompting complexity, culminating in a research agenda for studying which texts and behaviors are achievable from short prompts under a fixed LM interface.","arXiv :2607 .06 145v 1 [ cs .CL] 7 Jul 2026  \nPrompting Complexity  \nShortest Prompts for Texts and Behaviors in LLMs  \nAdrian Cosma  \nDalle Molle Institute for Artificial Intelligence (IDSIA)  \n[adrian.cosma@idsia.ch](adrian.cosma@idsia.ch)  \nAbstract  \nIn this paper, we define the quantity of prompting complexity: for a fixed instructiontuned language model, what is the shortest plausible prompt that makes deterministic decoding produce a target text? It is an LM-relative analogue of resourcebounded Kolmogorov complexity: the prompt is a program, the model interface is the interpreter, and information omitted from the prompt is supplied by the model’s weights, training distribution, tokenizer, template, and decoding rule. Unlike classical Kolmogorov complexity, this measure is intentionally non-universal.  \nIn the finite-context setting it is computable by enumeration, but there is no modelindependent invariance theorem; the same text may be cheap for one model and inaccessible or expensive for another. To keep the search space aligned with prompt engineering, we restrict programs to plausible human-readable texts rather than arbitrary token strings. We extend the exact definition to soft prompting complexity for approximate outputs, yielding a lossy notion of model-relative text compression and a formal target for prompt optimization. We also define prompting distance by comparing shortest generating prompts, and behavioral prompting complexity for reaching any output satisfying a specification. Based on these formulations, we define a research agenda for empirically studying which texts and behaviors are accessible from short plausible prompts under a fixed LM interface.  \n1 Introduction  \nLanguage models (LMs) have made prompt engineering a routine interface for computation in natural language. A user does not directly program the model’s weights, tokenizer, decoding rule, or training distribution; instead, they write a short text and hope that, under the fixed model, it causes the desired completion. This exposes a more basic theoretical question: given a target text what is the shortest plausible prompt that causes a fixed language model to generate it? Furthermore, there are cases in which the target text is not relevant to the user, but the model’s behavior is: given a target behavior class, what is the shortest plausible prompt that causes a fixed language model to exhibit it? We formalize these questions as prompting complexity and behavioral prompting complexity, respectively.  \nIntuitively, prompting complexity measures how much information a user must supply to a model in order to elicit a desired output. This is a common situation in practice, as exemplified by the following scenario.  \nIntuition. Alice and Bob are two people who both rely on the same LM while emailing. Alice writes a few rough notes, asks the model to expand them into a polished message, and sends the long email. Bob then emails back by writing his own rough notes and then asking the same model to expand them. The long messages are mostly an interface convention: relative to the shared model, the useful information is defined by the short note together with the model’s generative capabilities. Prompting complexity asks how short such a note can be for a target text.  \nIn this scenario, the model’s learned expansion rule is a form of compression: it allows a user to supply a short prompt and have the model fill in the rest.  \nFigure 1: Illustration of prompting complexity concepts developed in this work. (top left) Prompting complexity Ψf (t) is the length of the shortest plausible prompt p ↣ t that causes the model f to output t. (top right) Soft prompting complexity Ψεf,d (t) is the length of the shortest prompt whose output lies within distance ε of t. (bottom left) Prompting distance dΨ (t1 , t2 ) compares two texts by comparing their shortest relaxed prompts. (bottom right) Behavioral prompting complexity Ψf (B)  \nis the length of the short","cbCaiuuKDWLnlPpA","https://ap.wps.com/l/cbCaiuuKDWLnlPpA","pdf",638906,3,1,23,"English","en",105,"# Introduction\n## Prompting complexity and behavioral prompting complexity\n## Illustration and core definitions\n# Plausible Texts","[{\"question\":\"What is prompting complexity in this work?\",\"answer\":\"Prompting complexity is defined as the length of the shortest plausible prompt that causes a fixed language model to generate a specific target text under deterministic decoding.\"},{\"question\":\"How does soft prompting complexity differ from prompting complexity?\",\"answer\":\"Soft prompting complexity measures the shortest prompt whose output lies within a distance ε of the target text, turning the notion from exact generation to approximate generation.\"},{\"question\":\"Why is the metric model-relative rather than universal?\",\"answer\":\"Because there is no model-independent invariance theorem: the same target text can be cheap for one model while inaccessible or expensive for another, given differences in weights, tokenizer, templates, and decoding 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is prompting complexity in this work?","Question",{"text":75,"@type":76},"Prompting complexity is defined as the length of the shortest plausible prompt that causes a fixed language model to generate a specific target text under deterministic decoding.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does soft prompting complexity differ from prompting complexity?",{"text":80,"@type":76},"Soft prompting complexity measures the shortest prompt whose output lies within a distance ε of the target text, turning the notion from exact generation to approximate generation.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is the metric model-relative rather than universal?",{"text":84,"@type":76},"Because there is no model-independent invariance theorem: the same target text can be cheap for one model while inaccessible or expensive for another, given differences in weights, tokenizer, templates, and decoding 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