Artificial Intelligence 2007 Spring Homework 1
Due date: March 22, 2007 March 15, 2007
1. Water Jug Problem
You are given two jugs with no measuring marks, a 4-gallon one and a 3-gallon one. There is a pump to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug? For the agent of water jug, develop a PEAS description of this task environment.
2. AIMA[3.8]
Consider a state space where the start state is number 1 and the successor function for state n returns two states, numbers 2n and 2n + 1.
a. Draw the portion of the state space for states 1 to 15.
b. Suppose the goal state is 11. List the order in which nodes will be visited for breadth-first search, depth-limited search with limit 3, and iterative deepening search.
c. Would bidirectional search be appropriate for this problem? if so, describe in detail how it would work.
d. What is the branching factor in each direction of the bidirectional search?
e. Does the answer to (c) suggest a reformulation of the problem that would allow you to solve the problem of getting from state 1 to a given goal state with almost no search?
3. AIMA[3.12]
Prove that uniform-cost search and breadth-first search with constant step costs are optimal when used with the GRAPH-SEARCH algorithm. Show a state space with varying step costs in which GRAPH-SEARCH using iterative deepening finds a suboptimal solution.
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