# Hoon Hong: Research Overview

## Goal

My current research goal is to develop
• mathematical theories
• algorithms
• software libraries/packages
for efficiently solving non-linear constraints, arising in science and engineering, and declarative language design.

A constraint is an expression (well formed formula) involving rational numbers, variables (ranging over real numbers), arithemetic functions such as +, -, * , /, relations such as =, >, >=, logical connectives such as and , or , not , quantifers such as forall and exists (formally a formula in the first order theory of real closef field).

A constraint defines a subset of the free variable space, we naturally calls it the solution set. Solving means to extract some useful information about the solution set such as
• Emptiness
• Finiteness
• Dimension
• Number of components
• Topological type
• Volume
• A defining quantifier-free formula
• An approximate simple defining formula.
• Plotting
• ....

## Motivation

The main motivation for tackling this problem comes from the observation that numerous problems in science and engineering can be reduced to that of solving constraints. Thus, making progress in solving constraints will have a significant impact on those areas.

## Approach

I try to achieve efficiency by
• Developing new/better mathematical theories and more efficient algorithms.
• Utilizing the structure (in particular composition).
• Allowing approximate answers (but to a given precision).
• Parallelism.