The document discusses various concepts related to defining and solving problems using state space representation and search algorithms. It defines a problem as any task or goal that can be represented precisely using an initial state, goal state, and applicable rules. Search algorithms like breadth-first search and depth-first search are described for systematically exploring the problem space. Heuristic search methods are discussed which use domain knowledge to guide the search.

1. PROBLEM, PROBLEM SPACE AND SEARCH

9. 4- Gallon jug 3- Gallon jug Rules 0 0 0 3 2 3 0 9 3 3 2 3+1=4 3-1=2 7 0 2 11 2 0

10. 4- Gallon jug 3- Gallon jug Rules 0 0 4 0 4-3=1 0+3=3 1 0 0 1 4 1 4-2=2 1+2=3

16. library school hospital factory park newsagent university church Explore nodes in tree order: library, school, hospital, factory, park, newsagent, uni, church. (conventionally explore left to right at each level)

32. Monotonic Repetition of rules is allowed Non-Monotonic No such Repetition is allowed Partially Commutative If x gives y then permutation of x also gives y Theorem Proving Robot Navigation Non Partially Commutative It is both monotonic and partial commutative Chemical Synthesis Bridge

34. Search Tree Search Graph 0,0 is appearing 2 times and it is one of our previous state so instead of repeating it we just linked it. It requires a small book-keeping which is called a graph. 0, 0 4, 0 0, 3 4, 3 0, 0 1, 3 4, 3 0, 0 3, 0 0, 0 4, 0 0, 3 4, 3 0, 0 1, 3 4, 3 0, 0 3, 0