Narrow Results

An enzyme system organized in a flow device with three parallel channels was used to mimic a reversible Double Feynman Gate (DFG) with three input and three output signals. Reversible conversion of NAD⁺ and NADH cofactors was used to perform XOR logic operations, while biocatalytic oxidation of NADH resulted in Identity operation working in parallel. The first biomolecular realization of a DFG gate is promising for integrating into complex biomolecular networks operating in future unconventional biocomputing systems, as well as for novel biosensor applications.

When signum operation is applied in chaotic systems to realize piecewise-linearity, the original nonlinearity turns to be a kind of Boolean calculation, and correspondingly the chaotic circuit can be implemented by an analog structure embedded with some logic-gate circuits. In this paper, as examples based on the diffusionless Lorenz system we proposed a couple of chaotic flows with signum piecewise-linearity, which experimentally resorts to digital gate circuits. The experimental chaotic circuit with logic elements was built, and the oscillation in the physical circuit agrees well with the numerical simulation.

A mathematical model of classical computer was invented by Alan Turing and named “Turing machine” model, which is an idealized computer with a simple set of instructions and infinite memories. Soon after Turing’s model was proposed, John von Neumann developed a theoretical model for how to implement all the components in a computer to be fully capable as a Turing machine. In more practical way, we will make use of the circuit model, which is useful also in the study of quantum computation. A circuit may involve many inputs, outputs, many wires and many logic gates. These circuits will be implemented by semi-conductors, which have two functions as conductor and insulator and acts under given conditions as a high-speed switch that leads and stops electricity. Modern computers such as personal computers (PC) use integrated circuits (IC) of semiconductor. While the peculiar feature of semiconductor is based entirely on physics of quantum mechanics, we do not call these computers “quantum computers” but rather called “classical computers”, because logic gates are based on binary representations and any quantum state of atom or molecule is not used as a logic gate: in classical computers, the data are represented by two logical values 0 and 1 in the circuits using devices with high voltage/low voltage, current on/off, and/or direction of magnetization up/down.

The following sections are included:

• Turing machine

• von Neumann computer

• Possibility and complexity of computation
  • Arithmetic operations
    • P problem
  • Factorization and decision of prime numbers
    • About the NP problem
  • Combination problem
    • NP-complete problems
  • Computational complexity and amount of computation

• Logic gates

• Logic circuits

• Sequential circuit and memory

• Problem