Sep 4, 2006
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- Review of homework #1 problems

- a new type of search: constraint satisfaction search
        - map-coloring
        - cryptarithmetic problems
        - 8-queens
	- Sudoku

- (All) CSPs have
        - Variables
        - Domains
        - Constraints
                - can summarize in the form of
                  constraint graph

- Whats the big deal?
	- must merely have to satisfy constraints
		=> typically no notion of optimality
        - goal test is not a black box
        	=> goal test can be decomposed

- CSPs hence have a nice structure
	- that can be exploited in search algorithms

- General framework of CSP
	- Variables: V_1, V_2, ... , V_n
	- Domains: D_1, D_2, ..., D_n
		- value of V_i belongs to D_i
	- Constraints: which are relations R_ij
		- allowable combinations of values for V_i and V_j

- Formulate CSP for both examples
	- 4-queens
		- V_i: column id of queen in the i-th row
		- D_i = {1,2,3,4}
		- Relations are such that
		  - no two queens in same row 
		     (default by encoding)
		  - no two queens in same column
                     (V_i <> V_j)
		  - no two queens in same diagonal
		     (|i-j| <> |V_i - V_j|)
	- easy to do for map coloring


- Types of constraints
	- unary
		=> variable cannot take certain value
	- binary
		=> examples from n-queens
	- n-ary
		=> example from cryptarithmetic

- Can always 
	- "simplify" out domains so that unary constraints not needed
	- convert n-ary to binary	
		=> hence, we focus on primarily binary constraints

- Relationships to database systems
	- if you are in CS4604, you will encounter same ideas
	  under "relationships"