Large Lukasiewicz Logic Arrays

Lukasiewicz logic arrays (LLAs) are analog VLSI circuits structured as trees of continuous-valued implications. First described in 1990, LLAs are now nding uses as applicationspeci c array processors for image processing, fuzzy inference, and robotic control. Yet an early question persists: Why do LLAs work? Intuitively, a small error should build up through successive implications of an arbitrarily deep Lukasiewicz logic array (LLA) and render the output unusable, yet LLAs fabricated in normal MOSIS runs are typically precise to 10 bits. Analog neural nets are comparably robust. We compared the information capacity of a 31-cell LLA and a baseline circuit consisting of simple wires. The results indicate that the LLA preserves approximately 3/4 bit less information per input than the baseline circuit. The magnitude of the error is not a function of the number of implications in the LLA. Functional and electrical simulations suggest that information loss in an LLA increases less than linearly with circuit size. Our hypothesis, based on information theory, is that random noise in one node partially cancels the error introduced by previous nodes. In arbitrarily large LLAs random noise acts to correct errors in analog values without having to encode them. The LLA is inherently and probabilistically error-correcting. We close by discussing circuits that we are fabricating to verify the hypothesis by measuring information loss at multiple points within an LLA.