DNA Implementation of Theorem Proving with Resolution Refutation in Propositional Logic

Theorem proving is a classical AI problem having a broad range of applications. Since its complexity grows exponentially with the size of the problem, many researchers have proposed methods to parallelize the theorem proving process. Here, we use the massive parallelism of molecular reactions to implement parallel theorem provers. In particular, we show that the resolution refutation proof procedure can be naturally and efficiently implemented by DNA hybridization. Novel DNA encoding schemes, i.e. linear encoding and hairpin encoding, are presented and their effectiveness is verified by biochemical experiments.

[1]  Masami Hagiya,et al.  From Molecular Computing to Molecular Programming , 2000, DNA Computing.

[2]  Melvin Fitting,et al.  First-Order Logic and Automated Theorem Proving , 1990, Graduate Texts in Computer Science.

[3]  Nils J. Nilsson,et al.  Artificial Intelligence: A New Synthesis , 1997 .

[4]  V. Mihalache.  Prolog approach to DNA computing , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[5]  Christian B. Suttner.  SPTHEO - A Parallel Theorem Prover , 2004, Journal of Automated Reasoning.

[6]  Masami Hagiya,et al.  Towards parallel evaluation and learning of Boolean μ-formulas with molecules , 1997, DNA Based Computers.

[7]  Piotr Wasiewicz,et al.  The Inference Based on Molecular Computing , 2000, Cybern. Syst..

[8]  Satoshi Kobayashi,et al.  Horn Clause Computation with DNA Molecules , 1999, J. Comb. Optim..

[9]  Natasa Jonoska,et al.  Self-assembling DNA graphs , 2004, Natural Computing.

[10]  Jules Moreau,et al.  Molecular Computation by DNA Hairpin Formation , 2000 .

[11]  R J Lipton,et al.  DNA solution of hard computational problems. , 1995, Science.

[12]  K Sakamoto,et al.  Molecular computation by DNA hairpin formation. , 2000, Science.

[13]  In-Hee Lee,et al.  Evolutionary sequence generation for reliable DNA computing , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[14]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[15]  Satoshi Kobayashi,et al.  Horn Clause Computation by Self-assembly of DNA Molecules , 2001, DNA.