TY - JOUR

T1 - DNA-based algorithms for learning Boolean formulae

AU - Sakakibara, Yasubumi

N1 - Funding Information:
We would like to thank Satoshi Kobayashi for his useful comments. This work is supported in part by Grant-in-Aid for Scientific Research (C) No. 13680464 and Grant-in-Aid for Scientific Research on Priority Area No. 14085205. This work was also performed in part through Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology, the Japanese Government.

PY - 2003

Y1 - 2003

N2 - We apply a DNA-based massively parallel exhaustive search to solving the computational learning problems of DNF (disjunctive normal form) Boolean formulae. Learning DNF formulae from examples is one of the most important open problems in computational learning theory and the problem of learning 3-term DNF formulae is known as intractable if RP ≠ NP. We propose new methods to encode any k-term DNF formula to a DNA strand, evaluate the encoded DNF formula for a truth-value assignment by using hybridization and primer extension with DNA polymerase, and find a consistent DNF formula with the given examples. By employing these methods, we show that the class of k-term DNF formulae (for any constant k) and the class of general DNF formulae are efficiently learnable on DNA computer. Second, in order for the DNA-based learning algorithm to be robust for errors in the data, we implement the weighted majority algorithm on DNA computers, called DNA-based majority algorithm via amplification (DNAMA), which take a strategy of "amplifying" the consistent (correct) DNA strands. We show a theoretical analysis for the mistake bound of the DNA-based majority algorithm via amplification, and imply that the amplification to "double the volumes" of the correct DNA strands in the test tube works well.

AB - We apply a DNA-based massively parallel exhaustive search to solving the computational learning problems of DNF (disjunctive normal form) Boolean formulae. Learning DNF formulae from examples is one of the most important open problems in computational learning theory and the problem of learning 3-term DNF formulae is known as intractable if RP ≠ NP. We propose new methods to encode any k-term DNF formula to a DNA strand, evaluate the encoded DNF formula for a truth-value assignment by using hybridization and primer extension with DNA polymerase, and find a consistent DNF formula with the given examples. By employing these methods, we show that the class of k-term DNF formulae (for any constant k) and the class of general DNF formulae are efficiently learnable on DNA computer. Second, in order for the DNA-based learning algorithm to be robust for errors in the data, we implement the weighted majority algorithm on DNA computers, called DNA-based majority algorithm via amplification (DNAMA), which take a strategy of "amplifying" the consistent (correct) DNA strands. We show a theoretical analysis for the mistake bound of the DNA-based majority algorithm via amplification, and imply that the amplification to "double the volumes" of the correct DNA strands in the test tube works well.

KW - Boolean formula

KW - Computational learning

KW - DNA computing

KW - Massively parallel

KW - Population computation

KW - Weighted majority

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U2 - 10.1023/A:1024982203756

DO - 10.1023/A:1024982203756

M3 - Article

AN - SCOPUS:4344662001

SN - 1567-7818

VL - 2

SP - 153

EP - 171

JO - Natural Computing

JF - Natural Computing

IS - 2

ER -