I present a survey of recent advances in the algorithmic and computational complexity theory of non-Boolean Quantified Constraint Satisfaction Problems, incorporating some more modern research directions. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems

The rigidity and flexibility of proteins is critical to what they do in the body, and how drugs can change this. Both too rigid and too flexibly proteins are the source of diseases in humans and predicting flexibility from a 3-D structural file is an important challenge. We present one computational approach, currently implemented at flexweb.asu.edu, based on the geometric, combinatorial and al...

Heribert Vollmer : Boolean functions and Post’s lattice with applications to complexity theory. A Boolean functions f can be obtained from a set B of Boolean functions by superposition, if f can be written as a nested composition of functions from B. In the 1940’s, Emil Post determined the complete list of all sets of Boolean functions closed under superposition, and for each of them, he constr...

During the past two decades, an impressive array of diverse methods from several different mathematical fields, including algebra, logic, analysis, probability theory, graph theory, and combinatorics, have been used to analyze both the computational complexity and approximabilty of algorithmic tasks related to the constraint satisfaction problem (CSP), as well as the applicability/limitations o...

Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. CHR programs consist of multi-headed guarded rules which allow to rewrite constraints into simpler ones until a solved form is reached. Many empirical evidences suggest that multiple heads augment the expre...

This is the final fifth paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. Here we consider interacting quantum field theories, specifically we consider the non – Abelean Gauss constraints of Einstein – Yang – Mills theory and 2+1 gravity. Interestingly, while Yang – Mills theory in 4D is not yet rigorousl...

I study a theoretical model of life-cycle portfolio choice for an investor who has an option to invest in human capital but is liquidity constrained. I find that, since the young are more likely to exercise the option than the old, they are more concerned about liquidity risk (i.e. the risk that the liquidity constraint binds when it is optimal to invest). This, in turn, implies a hump-shaped p...

While game theory is widely used to model strategic interactions, a natural question is where do the game representations come from? One answer is to learn the representations from data. If one wants to learn both the payoffs and the players’ strategies, a naive approach is to learn them both directly from the data. This approach ignores the fact the players might be playing reasonably good str...

We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems. 1998 ACM Subject Classification A.1 Introductory and Survey, D.3.2 Constraint and Logic Languages, F.2.2 Computations on Discrete Structures

The computational and descriptive complexity of finite domain fixed template constraint satisfaction problem (CSP) is a well developed topic that combines several areas in mathematics and computer science. Allowing the domain to be infinite provides a way larger playground which covers many more computational problems and requires further mathematical tools. I will talk about some of the resear...