1. State-Space Representation Read Chapter 3

2. Searches you use MapQuest –road maps Google –documents CiteSeer –research documents

3. Abstract Model Initial State Operators: maps a state into a next state –alternative: successors of state Goal Predicate: test to see if goal achieved Optional: –cost of operators –cost of solution

4. Representation Matters

5. 8-Queens Problem.1 Initial State: empty 8 by 8 board Operators: –add a queen to empty square –remove a queen –[move a queen to new empty square] Goal: no queen attacks another queen –all queens on board

6. 8-Queens Problem.2 Initial State: empty 8 by 8 board Operators: –add ith queen to some column (i = 1..8) –Ith queen is in row i Goal: no queen attacks another queen –8 queens on board

7. 8-Queens Problem.3 Initial State: –random placement of 8 queens ( 1 per row) Operators: –move a queen to new position Goal: no queen attacks another queen –8 queens on board

8. Minton Million Queens problem Can’t be solved by complete methods Easy by Local Improvement – –to be covered in 2 nd week Same method works for many real-world problems.

9. Traveling Salesman Problem Given: n cities and distances Initial State: fix a city Operators: –add a city to current path –[move a city to new position] –[swap two cities] –[UNCROSS] Goal: cheapest path visiting all cities once and returning.

10. TSP Clay prize: $1,000,000 if prove can be done in polynomial time or not. Number of paths is N! Similar to many real-world problems. Often content with best achievable: bounded rationality

11. Sliding Tile Puzzle 8 by 8 or 15 by 15 board Initial State: random (nearly) of number 1..7 or 1..14. Operators: –slide tile to adjacent free square. Goal: All tiles in order.

12. Cryptarithmetic SEND+MORE = MONEY Initial State: no variable has a value Operators: –assign a variable a digit (0..9) (no dups) –unassign a variable Goal: arithmetic statement is true. Example of Constraint Satisfaction Problem

13. Boolean Satisfiability (3-sat) Problem example (a1 +~a4+a7)&(….) Initial State: no variables are assigned values Operators –assign variable to true or false –negate value of variable (t->f, f->t) Goal: boolean expression is satisfied. $1,000,000 problem Ratio of clauses to variables breaks problem into 3 classes: –low ratio : easy to solve –high ratio: easy to show unsolvable –mid ratio: hard

14. Most Common Word Finding Given: word length + set of strings Find: most common word to all strings –Warning: word may be misspelled. length 5: hellohoutemary position 5 bargainsamhotseview position 10 tomdogarmyprogramhomse position 17 answer: HOUSE

15. Misspelled Word Finding Let pi be position of word in string i Initial state: pi = random position Operators: assign pi to new position Goal state: words defined by pi with lowest entropy. (or some other measure) Problem derived from Bioinformatics –finds regulatory elements; these determine whether gene are made into proteins.