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. Initial state 2. Description of action: successor function h(s) = set of action-state pairs 3. Goal test, can be Explicit Implicit 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

Question

1. Prove by induction that Vi > 1, (L*)' = L*. • Basis: ? • Inductive Hypothesis: ? • Complete the rest of the proof: ?

Answer 1

Question

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. Initial state

2. Description of action: successor function h(s) = set of action-state pairs

3. Goal test, can be

Explicit

Implicit

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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