AI-complete

In the field of artificial intelligence (AI), tasks that are hypothesised to require artificial general intelligence to solve are informally known as AI-complete or AI-hard. ^[1] Calling a problem AI-complete reflects the belief that it cannot 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]

AI-complete problems could be useful, for example, to test for the presence of humans as CAPTCHAs aim to do, and in computer security to circumvent brute-force attacks. ^{[3] [4]}

History

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]

Expert systems, that were popular in the 1980s, were able to solve very simple and/or restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempted to "scale up" their systems to handle more complicated, real-world situations, the programs tended to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they would fail as unexpected circumstances outside of its original problem context would begin to appear. When human beings are dealing with new situations in the world, they are helped by their awareness of the general context: they know what the 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. Expert systems lacked this adaptability and were brittle when facing new situations. ^[8]

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." ^[9] Similarly, some tasks once considered to be AI-complete, like machine translation, ^[10] are among the capabilities of large language models. ^[11]

AI-complete problems

AI-complete problems are hypothesized to include:

• AI peer review ^[12] (composite natural language understanding, automated reasoning, automated theorem proving, formalized logic expert system)
• Bongard problems ^[13]
• Computer vision (and subproblems such as object recognition) ^[14]
• Natural language understanding (and subproblems such as text mining, ^[15] machine translation, ^[16] and word-sense disambiguation ^[17] )
• Autonomous driving ^[18]
• Dealing with unexpected circumstances while solving any real world problem, ^[19] whether it's navigation or planning or even the kind of reasoning done by expert systems.^{[ citation needed ]}

Formalization

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 formalization yet, conventional complexity theory does not enable to formally define AI-completeness.

To address this problem, a complexity theory for AI has been proposed. ^[20] 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 ${\displaystyle \langle \Phi _{H},\Phi _{M}\rangle }$, where the first element represents the complexity of the human's part and the second element is the complexity of the machine's part.

Results

The complexity of solving the following problems with a human-assisted Turing machine is: ^[20]

• Optical character recognition for printed text: ${\displaystyle \langle O(1),poly(n)\rangle }$
• Turing test:
  • for an ${\displaystyle n}$-sentence conversation where the oracle remembers the conversation history (persistent oracle): ${\displaystyle \langle O(n),O(n)\rangle }$
  • for an ${\displaystyle n}$-sentence conversation where the conversation history must be retransmitted: ${\displaystyle \langle O(n),O(n^{2})\rangle }$
  • for an ${\displaystyle n}$-sentence conversation where the conversation history must be retransmitted and the person takes linear time to read the query: ${\displaystyle \langle O(n^{2}),O(n^{2})\rangle }$
• ESP game: ${\displaystyle \langle O(n),O(n)\rangle }$
• Image labelling (based on the Arthur–Merlin protocol): ${\displaystyle \langle O(n),O(n)\rangle }$
• Image classification: human only: ${\displaystyle \langle O(n),O(n)\rangle }$, and with less reliance on the human: ${\displaystyle \langle O(\log n),O(n\log n)\rangle }$.

Research

Roman Yamopolsky ^[21] suggests that a problem ${\displaystyle C}$ is AI-Complete if it has two properties:

• It is in the set of AI problems (Human Oracle-solvable).
• Any AI problem can be converted into ${\displaystyle C}$ by some polynomial time algorithm.

On the other hand, a problem ${\displaystyle H}$ is AI-Hard if and only if there is an AI-Complete problem ${\displaystyle C}$ that is polynomial time Turing-reducible to ${\displaystyle H}$. This also gives as a consequence the existence of AI-Easy problems, that are solvable in polynomial time by a deterministic Turing machine with an oracle for some problem.

Yamopolsky ^[22] has also hypothesized that the Turing Test is a defining feature of AI-completeness.

Groppe and Jain ^[23] classify problems which require artificial general intelligence to reach human-level machine performance as AI-complete, while only restricted versions of AI-complete problems can be solved by the current AI systems. For Šekrst, ^[24] getting a polynomial solution to AI-complete problems would not necessarily be equal to solving the issue of strong AI, while emphasizing the lack of computational complexity research being the limiting factor towards achieving artificial general intelligence.

For Kwee-Bintoro and Velez, ^[25] solving AI-complete problems would have strong repercussions on the society.

See also

• ASR-complete
• List of unsolved problems in computer science
• Synthetic intelligence
• Practopoiesis

References

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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. http://cecs.louisville.edu/ry/TuringTestasaDefiningFeature04270003.pdf Archived 2013-05-22 at the Wayback Machine
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