Machine-rules of grammar

The sciences of numerical analysis and operations research reveals that, in order to facilitate the lowest number of denominations to ensure the highest values (via combinations), the instituted mint mints/prints the Re. 1, Rs. 2, Rs. 5, Rs. 10, Rs. 20, Rs. 50, Rs. 100, Rs. 500 and Rs. 1000 notes. Similarly, and I don't think it must be too much of a stretch to assume so, that in order to facilitate the most complex of logical constructs, a comparatively finite number of givens should prove sufficient.

For example, a half-adder in a computer is composed of an AND gate and a XOR gate; the XOR gate, in turn, looks like this:

[caption id="attachment_6881" align="aligncenter" width="393" caption="A XOR gate composed solely of MOSFETs"][/caption]

Therefore, from the diagram, a finite number of MOSFETs (each the constitution of a finite amount of logical information) can be seen to be employed to result in the output-logic. From this example, it is also deducible that such an approach to construction becomes invalidated when there is a (direct or indirect) violation of the third law of thermodynamics.

To illustrate the relation, an example exists in the form of the ADR (adiabatic demagnetization refrigerator) wherein a paramagnetic material is repeatedly isothermal magnetized and isentropically demagnetized. Such a machine cannot be used to reduce the temperature of the system to absolute zero because an isothermal process is involved in the refrigeration process - a condition mandated by both the Third Law and Nernst's Law (of heat transfer).

Similarly, if an inclusion of the component, C, available to us cannot result in the logical output, L, that we require, then the stated approach becomes useless. In other words, if the employment of a capacitor in even numbers presents a logical restriction in building a certain gate, then that particular component should be further broken before it is re-included into the project: if each capacitor consists of 2 Xs, then the overall logic shouldn't be defined as N-times-1.5C but N-times-3X.

To be continued...