APPROPRIATE APPLICATIONS

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Most human-important problems are qualitative: we neither have complete and precise input, nor do we want precise output of instances of solutions. Rather, we need qualitative information about the system, its general dependence on controls, and discovery of unexpected features. Problems in the following areas are often of this kind: artistic expression, climate and weather, control, engineering, image processing, pattern recognition, language, biology, physiology and medicine, physics, politics, and psychology.

As an example, consider the challenge of planning for global climate change. This system has many aspects that would make it a good candidate for the kind of approach we describe here. What we seek is relatively coarse simulations that generate scenarios, together with indicators of their dependence on controls (e.g., petroleum exhaustion, introduction of nuclear energy, deforestation, land use changes, etc.), rather than a detailed high precision description of a single instance.

Appropriate applications of this approach will have

the following characteristics:

(1) The problem is important;

(2) Input data is qualitative, incomplete, ambiguous;

(3) Physical models probably do not exist;

(4) The system behavior is complex;

(5) The system behavior contains structure and patterns;

(6) The behavior has both local and global character;

(7) It involves numerous dynamic processes;

(8) The system may exhibit catastrophes or discontinuities;

(9) The dynamics may be chaotic;

(10) Conventional computers can’t solve the problem;

(11) The behavior has structure;

(12) We do not need detailed precise data as output;

(13) We want to understand the system in order to control it;

(14) We would like to have real-time interactivity;

(15) We don’t care about the details.

Nanologic was conceived specifically to find a strategy for dealing with such problems. The combination of analog nanoelectronic reconfigurable arrays manipulating set-level data within an architecture that is the topological equivalent of the problem defines more than a potentially big industry; we believe it offers a possible path to meaningful attack on such problems. Applications appropriate for nanologic will have some, or all, of these characteristics. Probably the more of these characteristics it has, the greater will be the advantage of nanologic over conventional digital computers.

It may be asked how we can specify circuits and problems in this seemingly vague, nonspecific domain. The answer is inherent in the topological foundation of this approach: we are not demanding numerical agreement of a simulation with a real physical system, but the qualitative behavior of a set of systems connected by control parameters. Thus, we can be rather cavalier in the details; we can miss the behavior quantitatively by a lot, but we look for qualitative aspects of the behavior, in the hope and expectation that the simulation will give us some insight into the behavior of the system and how to control it. We need not be concerned with whether the fragments agree in detail with a real physical system. Although this may sound hopelessly sloppy, it is not; it is in fact the central motive for attacking intractable simulations, namely to find out (roughly) “what’s happening.”

Chaotic dynamical systems is exemplary of the large class of problems that cannot be solved with conventional digital computers but might be successfully attacked with the present approach. Diverse systems can be cast into the form of a chaotic dynamical system.

Nanologic derives much of its exceptional advantages from the casting of the computational algorithm into an electronic analog circuit that is a physical analogue of the system being simulated. The two systems are, by design, topological equivalents. It is the topological match between human-important problems and analog electronic circuits that enables nanologic to be realized and to have practical advantages over conventional digital computers.