The error-bounded descriptional complexity of approximation networks

The error-bounded descriptional complexity of approximation networks

It is well known that artificial neural nets can be used as approximators of any continuous functions to any desired degree and therefore be used e.g. in high speed, real-time process control. Nevertheless, for a given application and a given network architecture the non-trivial task remains to determine the necessary number of neurons and the necessary accuracy (number of bits) per weight for ...

Descriptional Complexity of Error Detection

The neighbourhood of a language L consists of all strings that are within a given distance from a string of L. For example, additive distances or the prefixdistance are regularity preserving in the sense that the neighbourhood of a regular language is always regular. For error detection and error correction applications an important question is to determine the size of the minimal deterministic...

Descriptional Complexity of Bounded Context-Free Languages

Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear contextfree languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-...

Descriptional Complexity of Error/Edit Systems

Sample Complexity versus Approximation Error

We consider the problem of learning an unknown real valued function from a sequence of values of the function at randomly chosen points when the estimates are constrained to some class of functions called the hypothesis class Ideally the hypothesis class should be able to approximate a wide variety of target functions yet not need an excessive number of examples to ensure that a learning algori...