Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 3, Problem 29E
Program Plan Intro

Admissible heuristic:

  • A heuristic h(s) is admissible, if for every node n, h(s)h*(s) is the true cost to reach the goal state from n
  • An admissible heuristic never over estimates the cost to reach the goal. That is optimistic. Sensorless search problem defines by four items. That are given below,
    1. 1. Initial state
    2. 2. Description of action: successor function h(s) = set of action-state pairs
    3. 3. Goal test, can be
      • Explicit
      • Implicit
    4. 4 Path cost. It reflects the performance measure.
  • An admissible heuristic can be obtained by taking maximum of h*(s). Since any sequences of actions that solve all states would solve each state, this heuristic is admissible.

Inconsistent heuristic:

  • A heuristic function is said to be inconsistent in the analysis of path-finding problems in artificial intelligence, if its approximation is always greater than to the approximate distance from any neighbouring vertex to the target.
  • Inconsistent heuristic can be represented as,

h(N)>c(N,p)+h(p)

where,

  • h is the consistent heuristic function
  • N is any node of the graph
  • P is any decedent of N
  • G is the goal node
  • c(N,P) is the cost of reaching node P from N

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Students have asked these similar questions
1. Prove by induction that Vi > 1, (L*)' = L*. • Basis: ? • Inductive Hypothesis: ? • Complete the rest of the proof: ?
3. The statement "3x E Z such that ¢ Q" is clearly false, but the statement "3x ER such that x 4 Q" is true. This shows that the domain of the quantifier matters. Now, give your own sim- ple example for the predicate P(x) such that "x E Z such that P(x)" is false but “x E R such that P(x)" is true. Avoid very similar predicates like "x ¢ Z" or "2x ¢ Q" as your answer.2
Assume that a rook can move on a chessboard any number of squares in a straight line,vertically or horizontally, but cannot jump over other pieces.A. Give two possible admissible heuristics.B. Which one is more informed than the other (dominates the other). Explain your answer.C. Explain how we can combine the two heuristics in such a way the give a better heuristic thatis still admissible.
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