Dynamical Recognizers: Real-Time Language Recognition by Analog Computers

We consider a model of analog computation which can recognize various languages in real time. We encode an input word as a point in Rd by composing iterated maps, and then apply inequalities to the resulting point to test for membership in the language. Each class of maps and inequalities, such as quadratic functions with rational coe cients, is capable of recognizing a particular class of languages for instance, linear and quadratic maps can have both stack-like and queue-like memories. We use methods equivalent to the VapnikChervonenkis dimension to separate some of our classes from each other, e.g. linear maps are less powerful than quadratic or piecewise-linear ones, polynomials are less powerful than elementary (trigonometric and exponential) maps, and deterministic polynomials of each degree are less powerful than their non-deterministic counterparts. Comparing these dynamical classes with various discrete language classes helps illuminate how iterated maps can store and retriev...

• Type: Journal
• Year: 1998
• Where: TCS
• Authors: Cristopher Moore
• Keywords: Analog Computation, Quadratic Maps, Rational Coe Cients, TCS 1998, Theoretical Computer Science