## State Space – Key to the Art of Good Design

Posted by mike keating on June 23rd, 2009

There is a conventional argument that complete verification is impossible. It goes like this: even a simple design of 100 flops has a state space of 2^100, which, simulating at a GHz, would take longer than the life of the universe to completely test. This argument raises some important points.

One key point is that verification is the hardest problem in chip design and in EDA. It is NP-complete, like many other problems in EDA, such as optimization. But it is the one problem for which we do not have heuristics that give us a “good enough” solution. Therefore we must keep the state space of a design as small as possible – the only practical way to manage NP complete problems.

Another key point is that a state space of 2^100 is clearly too large for any human to understand. So we are developing designs no one understands. This can’t be good!

In my experience, most designs can be refactored to reduce the state space by orders of magnitude. By parititioning the design well we can make the resulting state space much easier to understand. In fact, improving how we manage design state space is the key to improving how we do design and verification.

Chapter 4 of the Art of Good Design discusses this key issue of state space management.

The discussion of complete verification of IC chip design may be looked at through the mathematical model approach. A design needs validity measured through a multiplicity of facts, but one way to study circuits is the original reductive atomic topological function concept. That basis is the only way to build a chip simulation of strict relative quantum topological electron and photon flow specifications.

In other words, if a virtual circuit is tested by many parameters the model’s physics are the decisive argument generating the data. However, only an exact, 3D data point image of the material’s force and energy fields, waves, and rays will suffice to make significant judgements about current, impedance, switching, or other component functionality. That is true because plainly the quantized texture of electromagnetic energy or heat will always defy the intuition or estimations of observers.

In fact, relativistic Lorenz-Einstein transform functions for time, mass, and energy must be integrated into the workon quantized wave equations for frequency and wavelength to derive a coherent RQT (relative quantum topological) Schrodinger wavefunction of one atom. One way to achieve this is by the RQT series differential expansion of the Schrodinger equation. While the atom, psi(z), pulsates at {Nhu=e/h} by {e=m(c^2)} transform of nuclear mass to radiative forcons with valid joule values in cycles of nuclear emission and absorption, it’s reactions are limited only by space and time.

While space is taken as bonded to psi by gravity the atom pulsates by a series differential for varying rates of nucleoplastic surface transformation in a process limited by gravity time boundaries. Quantum symmetry numbers are assigned along the series to lend 3D topology to the model. That composes the GT integral atomic function.

When psi’s internal momentum function is written, rearranged to the photon gain rule and integrated for GT boundaries a set of 26 topological wavefunctions is found, each the image of an energy intermedon of the psi’s 5/2 kT J internal heat capacity energy cloud, which has only those 26 types of particles in it. Those intermedon values intersect the sizes of the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton, k, 5/2 k, 3/2 k. The result is an exact picoyoctometric 3D animated interactive video atomic model image for force and energy fields with the complete waveset.

Images of the h-bar magnetic energy waveparticle of ~175 picoyoctometers are available at http://www.symmecon.com, with essays, graphics and the book The Crystalon Door, complete guide to MAVCAM (molecular or material animated video computer assisted modeling).

The discussion of complete verification of IC chip design may be looked at through the mathematical model approach. A design needs validity measured through a multiplicity of facts, but one way to study circuits is the original reductive atomic topological function concept. That basis is the only way to build a chip simulation of strict relative quantum topological electron and photon flow specifications.