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In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems, assuming intelligence is computational, is equivalent to that of solving the central artificial intelligence problem—making computers as intelligent as people, or strong AI.[1] To call a problem AI-complete reflects an attitude that it would not be solved by a simple specific algorithm.

AI-complete problems are hypothesised to include computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real-world problem.[2]

Currently, AI-complete problems cannot be solved with modern computer technology alone, but would also require human computation. This property could be useful, for example, to test for the presence of humans as CAPTCHAs aim to do, and for computer security to circumvent brute-force attacks.[3][4]


The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of difficult problems.[5] Early uses of the term are in Erik Mueller's 1987 PhD dissertation[6] and in Eric Raymond's 1991 Jargon File.[7]

AI-complete problems[edit]

AI-complete problems are hypothesized to include:

Machine translation[edit]

To translate accurately, a machine must be able to understand the text. It must be able to follow the author's argument, so it must have some ability to reason. It must have extensive world knowledge so that it knows what is being discussed — it must at least be familiar with all the same commonsense facts that the average human translator knows. Some of this knowledge is in the form of facts that can be explicitly represented, but some knowledge is unconscious and closely tied to the human body: for example, the machine may need to understand how an ocean makes one feel to accurately translate a specific metaphor in the text. It must also model the authors' goals, intentions, and emotional states to accurately reproduce them in a new language. In short, the machine is required to have wide variety of human intellectual skills, including reason, commonsense knowledge and the intuitions that underlie motion and manipulation, perception, and social intelligence. Machine translation, therefore, is believed to be AI-complete: it may require strong AI to be done as well as humans can do it.

Software brittleness[edit]

Current AI systems can solve very simple and/or restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempt to "scale up" their systems to handle more complicated, real-world situations, the programs tend to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they fail as unexpected circumstances outside of its original problem context begin to appear. When human beings are dealing with new situations in the world, they are helped immensely by the fact that they know what to expect: they know what all things around them are, why they are there, what they are likely to do and so on. They can recognize unusual situations and adjust accordingly. A machine without strong AI has no other skills to fall back on.[13]

DeepMind published a work in May 2022 in which they trained a single model to do several things at the same time. The model, named Gato, can "play Atari, caption images, chat, stack blocks with a real robot arm and much more, deciding based on its context whether to output text, joint torques, button presses, or other tokens."[14]


Computational complexity theory deals with the relative computational difficulty of computable functions. By definition, it does not cover problems whose solution is unknown or has not been characterised formally. Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.

To address this problem, a complexity theory for AI has been proposed.[15] It is based on a model of computation that splits the computational burden between a computer and a human: one part is solved by computer and the other part solved by human. This is formalised by a human-assisted Turing machine. The formalisation defines algorithm complexity, problem complexity and reducibility which in turn allows equivalence classes to be defined.

The complexity of executing an algorithm with a human-assisted Turing machine is given by a pair , where the first element represents the complexity of the human's part and the second element is the complexity of the machine's part.


The complexity of solving the following problems with a human-assisted Turing machine is:[15]

  • Optical character recognition for printed text:
  • Turing test:
    • for an -sentence conversation where the oracle remembers the conversation history (persistent oracle):
    • for an -sentence conversation where the conversation history must be retransmitted:
    • for an -sentence conversation where the conversation history must be retransmitted and the person takes linear time to read the query:
  • ESP game:
  • Image labelling (based on the Arthur–Merlin protocol):
  • Image classification: human only: , and with less reliance on the human: .

See also[edit]


  1. ^ Shapiro, Stuart C. (1992). Artificial Intelligence In Stuart C. Shapiro (Ed.), Encyclopedia of Artificial Intelligence (Second Edition, pp. 54–57). New York: John Wiley. (Section 4 is on "AI-Complete Tasks".)
  2. ^ Roman V. Yampolskiy. Turing Test as a Defining Feature of AI-Completeness. In Artificial Intelligence, Evolutionary Computation and Metaheuristics (AIECM) --In the footsteps of Alan Turing. Xin-She Yang (Ed.). pp. 3-17. (Chapter 1). Springer, London. 2013.
  3. ^ Luis von Ahn, Manuel Blum, Nicholas Hopper, and John Langford. CAPTCHA: Using Hard AI Problems for Security Archived 2016-03-04 at the Wayback Machine. In Proceedings of Eurocrypt, Vol. 2656 (2003), pp. 294-311.
  4. ^ Bergmair, Richard (January 7, 2006). "Natural Language Steganography and an "AI-complete" Security Primitive". CiteSeerX {{cite journal}}: Cite journal requires |journal= (help) (unpublished?)
  5. ^ Mallery, John C. (1988), "Thinking About Foreign Policy: Finding an Appropriate Role for Artificially Intelligent Computers", The 1988 Annual Meeting of the International Studies Association., St. Louis, MO{{citation}}: CS1 maint: location missing publisher (link).
  6. ^ Mueller, Erik T. (1987, March). Daydreaming and Computation (Technical Report CSD-870017) PhD dissertation, University of California, Los Angeles. ("Daydreaming is but one more AI-complete problem: if we could solve anyone artificial intelligence problem, we could solve all the others", p. 302)
  7. ^ Raymond, Eric S. (1991, March 22). Jargon File Version 2.8.1 (Definition of "AI-complete" first added to jargon file.)
  8. ^ Strat, Thomas M.; Chellappa, Rama; Patel, Vishal M. (2020). "Vision and robotics". AI Magazine. 42 (2): 49–65. doi:10.1609/aimag.v41i2.5299. S2CID 220687545 – via ABI/INFORM Collection.
  9. ^ Krestel, Ralf; Aras, Hidir; Andersson, Linda; Piroi, Florina; Hanbury, Allan; Alderucci, Dean (2022-07-06). "3rd Workshop on Patent Text Mining and Semantic Technologies (PatentSemTech2022)". Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval. Madrid Spain: ACM. pp. 3474–3477. doi:10.1145/3477495.3531702. ISBN 978-1-4503-8732-3. S2CID 250340282.
  10. ^ Orynycz, Petro (2022), Degen, Helmut; Ntoa, Stavroula (eds.), "Say It Right: AI Neural Machine Translation Empowers New Speakers to Revitalize Lemko", Artificial Intelligence in HCI, Lecture Notes in Computer Science, Cham: Springer International Publishing, vol. 13336, pp. 567–580, doi:10.1007/978-3-031-05643-7_37, ISBN 978-3-031-05642-0, retrieved 2023-04-15
  11. ^ Ide, N.; Veronis, J. (1998). "Introduction to the special issue on word sense disambiguation: the state of the art" (PDF). Computational Linguistics. 24 (1): 2–40. Archived (PDF) from the original on 2022-10-09.
  12. ^ Musk, Elon (April 14, 2022). "Elon Musk talks Twitter, Tesla and how his brain works — live at TED2022". TED (conference) (Interview). Interviewed by Chris_Anderson_(entrepreneur). Vancouver.
  13. ^ Lenat, Douglas; Guha, R. V. (1989), Building Large Knowledge-Based Systems, Addison-Wesley, pp. 1–5
  14. ^ "A Generalist Agent". Retrieved 2022-05-26.
  15. ^ a b Dafna Shahaf and Eyal Amir (2007) Towards a theory of AI completeness Archived 2020-11-07 at the Wayback Machine. Commonsense 2007, 8th International Symposium on Logical Formalizations of Commonsense Reasoning.