A Mathematical Architecture for Molecular Computing

Traditional computing uses transistors and binary logic in order to perform computing operations. This approach has proved successful as long as the number of transistors per integrated circuit can be scaled to accommodate increasing speed and heat requirements. Unfortunately, this approach does not allow speeds above the limit where the size of the transistors approaches the limit of the integrated circuit substrates' molecular size. In this condition, electrons cannot reliably be contained within the boundaries separating one transistor from the next and increasingly small circuits become impractical. The current solution to this dilemma is to increase the number of functional units on an integrated circuit and thereby eliminate the need for increasingly small transistors. However whether we increase the number of functional units or the speed, there are inherent limitations in the number of transistors we can put onto one chip. We therefore look to another functional approach to generate the next generation of integrated circuits. We therefore look to using the molecules and elementary particles themselves as a means of computation. In order to accomplish molecular computation we need to modify the model of traditional computation from a transistor based binary method to analog based arbitrary basis model. This approach is not unknown since optical computation among other has used analog processing for highly parallel computation. The issue with molecular and quantum computing methods has traditionally been that understanding the state the computing function itself is often subject to high degree uncertainty. This uncertainty is not unexpected since the number of possible states that can exist when electromagnetic energy interrogates a collection of molecules, atoms, or electrons is quite large. In order to develop a method of representing these states we use a partially observable Markov decision process. We will then develop a finite state machine approach to computation based on a model for our molecular or quantum system.