we propose to explore this fascinating landscape inside np from the perspective of computational geometry, Guided by three complementary questions:(a) what can we say about the complexity of search problems derived fromexistence theorems in discrete geometry These problems offer a new perspective on

complexity classes previously studied in algorithmic game theory (ppad, Pls, Cls).

His topics are basic ideas of classical and quantum computational models and

complexity classes, mathematical tools and simple quantum mechanics required for quantum computing, quantum gates and quantum circuits, quantum algorithms, quantum error correction, quantum teleportation and superdense coding, and quantum cryptography.

Complexity classes in communication complexity theory.

Complexity classes for one-variable complexity functions, such as [THETA](g(n)), O(g(n)), [OMEGA](g(n)), o(g(n)), [omega](g(n)) are presented in almost every material that includes elements of the theory of complexity; see, for example, (Knuth, 1997), (Cormen et al.

In this paper we define five new complexity classes for multi-variable complexity functions and we prove some properties of these new defined classes.

In Section 2, we remind the definitions of the complexity classes for one-variable complexity functions and we give the definitions for five new complexity classes for multi-variable complexity functions.

Today,

complexity classes are central objects of study, and many results and problems in complexity theory are expressed in terms of

complexity classes.

This will allow for comparison of

complexity classes defined from different computational paradigms (e.

The fact that we use circuits to present these POMDPs is primarily a matter of convenience, for showing that the problems in question are members of their respective complexity classes.

The following Section 2 presents a short overview of the complexity classes we use, and gives the formal definitions of partially observable Markov Decision Processes, their different specification parameters, and the related decision problems.

We propose to contribute to this line of research in a number of interrelated directions, such as: studying new regularity properties (relevant to other fields of mathematics), developing abstract frameworks for such properties, studying higher

complexity classes, and generalising results to spaces other than the classical real numbers.

They have strong consequences concerning separation of

complexity classes, but only a few special cases have been proved.