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• W20776095 abstract "It is shown that optimal text compression is a harder problem than artificial intelligence as defined by Turing’s (1950) imitation game; thus compression ratio on a standard benchmark corpus could be used as an objective and quantitative alternative test for AI (Mahoney, 1999). Specifically, let L, M, and J be the probability distributions of responses chosen by a human, machine, and human judge respectively to the judge’s questions in the imitation game. The goal of AI is M = L, the machine is indistinguishable from human. But the machine wins (the judge guesses that it is human) when HJ(M) < HJ(L), where HQ(P) ≡ −Σx P(x) log Q(x) is the cross entropy of Q with respect to P. This happens when J is a poor estimate of L, meaning that the interrogator fails to anticipate the human’s responses, but even in the worst case when J = L, the machine can still win with a suboptimal solution (M ≠ L) by deterministically favoring the most likely responses over the true distribution. In contrast, optimal compression of a probabilistic language L with unknown distribution (such as English) using an estimated distribution M (an encoding of length −log2 M(x) bits for each string x) is M = L, by the discrete channel capacity theorem (Shannon, 1949). Answering questions in the Turing test (What are roses?) seems to require the same type of real-world knowledge that people use in predicting characters in a stream of natural language text (Roses are ___?), or equivalently, estimating L(x) for compression. Shannon (1951), and Cover and King (1978) established an upper bound of 1.3 bits per character (bpc) for the entropy (information content) of English narrative in a 27character alphabet (A-Z and space) using human prediction tests. No compression program has achieved this. Seven programs, including those top-rated by Gilchrist (1998) and Bell (1998) were used to compress English narrative, Alice in Wonderland (alice30.txt from the Gutenberg press, minus header) and Far from the Madding Crowd by Thomas Hardy (book1 from the Calgary corpus), after reducing both to 27 characters. The best compression was achieved by rkive 1.91b1: 1.86 bpc on alice and 1.94 on book1. Others tested (from worst to best) were compress 4.3d, pkzip 2.04e, gzip 1.2.4, ha 0.98, szip 1.05x, and boa 0.58b. All program options were set for maximum compression. Better compressors “learn”, using prior input to improve compression on subsequent input. szip was the best learner, compressing book1 to about 95% of the size of the two halves compressed separately. The first figure below shows the correlation between compression and learning. Similar results were obtained for alice. It was also found that better compressors make greater use of the syntactic and semantic constraints of English. Lexical," @default.
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• W20776095 title "Text compression as a test for artificial intelligence" @default.
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