Arithmetical Computation Via Self-Assembly Of DNA

It is the "Use of horizontal chain reaction for DNA-based addition", in the magazine "Science" pronounced by Frank Guamieri in 1996, starting the work of Algebra DNA-based Computation. At the same time, "entirely enumeration and automatic selection" in this paper became the basic idea of Algebra DNA-based Computation. Directed by that idea, we developed four DNA-base Computation model about basic Algebra operation.First, with the coding idea of Thomas H. Labean "Logical computation using DNA molecules", we developed a DNA-based addition model of two N-system addend. This arithmetic cast off serial addition idea, but entirely enumerate every pair of addends on a bit. And it also calculate two possible receiving carry value on each bit. So the addition can be operated through automatic selection , and complete collateral addition and carry operation.The second Algebra DNA-based Computation model is about numeral switch. Because many results is about the DNA-based Computation model of bi-system, when the question of numeral switch is done, we can indirectly resolve Algebra DNA-based Computation model of other numeral system. Numeral switch warehouse is the kernel of this algorithmic. With the idea of entirely enumeration, we make each bit coded for different system switching, and the coding satisfied definite rule which cause each bit arbitrary can link in order.The third is about DNA-based Computation model of multi-addend success addition. To resolve multiplication DNA-based Computation model, we must solve success addition in the computation process at first. At Chapter four, we introduce two kinds of DNA-based Computation model of success addition. The first is base on Labean's idea of Logical computation. And the second impose numeral switch warehouse.Finally, with the multiplication warehouse we can resolve the multiplication between one bit number and multi-bit number. In the multiplication warehouse, there have entirely enumeration of each pair of multiplier and multiplicand. This arithmetic could select different sub-warehouse base on different multiplier and multiplicand.