Syllabus

1. Decision problems in discrete domains.
2. Problem Modelling.
   a. Finite vs. Boolean domains.
   b. Constraints and constraint networks.
   c. Declarative modelling languages.
3. Problem Solving.
   a. Constraint Propagation.
   b. Consistency and algorithms for its maintenance.
   c. Integration with Backtracking.
   d. Advanced techniques: Intelligent backtracking (in SAT).
   e. Heuristics.
4. Introduction to Interval Constraints
   Continuous Constraints Satisfaction Problems
   Continuous Constraint Reasoning
   Solving Continuous Constrants

5. Continuous Constraints and Interval analysis.
   a. Representation of continuous domains
   b. Interval arithmetic.
   c. Interval Functions.
6. Interval Newton Method
  a. Newton Method for finding roots of univariate functions
  b. Interval extension of the Newton method
  c. Properties of the Interval Newton method
  d. Enclosing the zeros of a family of functions
7. Associating Narrowing Functions to Constraints
   a. Projection function and their enclosure
   b. Constraint decomposition method
   c. Constraint Newton method
   d. Complementary approaches
8. Constraint Propagation and Consistency Enforcement.
   a. Consistency Types (arc, interval, hull and box).
   b. Constraint Propagation.
   c. Narrowing Functions and their Properties.
   d. Constraint Propagation Algorithm and its Properties
9. Problem Solving in Continuous Domains.
   a. Modelling techniques.
   b. Languages and tools.
   c. Benchmarks