Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

A
B
AND
C D
E AND Y
Fig. 1.12: A Petri-like net representing non-determinism in a reasoning system
with initial states A and B and goal state Z.
Principle for testing determinism: After deriving the goal state
from the initial states, continue marking (backtracking) the parents of each
node starting from the goal node, until the initial states are reached. If
unmarked nodes are detected, then the system is non-deterministic; otherwise
it is deterministic. It may be noted that testing of determinism in a
knowledge-based system, for any set of starting and goal states, is a distinct
problem and no conclusion about determinism can be drawn for modified
initial or goal states.
The principle for testing determinism in the proposed knowledge-based
system is illustrated here with reference to the dependence graph (Petri-like
net) of fig.1.12. It may be noted that while backtracking on the graph, node
D is not marked and thus the system is non-deterministic.
Besides reasoning, non-determinism plays a significant role in many
classical AI problems. The scope of non-determinism in heuristic search has
already been mentioned. In this section, we demonstrate its scope in
recognition problems through the following example.
Example 1.3: This example illustrates the differences of deterministic and
non-deterministic transition graphs [9], called automata. Let us first consider
the problem of recognition of a word, say, “robot”. The transition graph (fig.
1.13(a)) for the current problem is deterministic, since the arcs emerging out
from a given state are always distinct. However, there exist problems, where
the arcs coming out from a state are not always distinct. For instance,
consider the problem of recognizing the words “robot” and “root”. Here, since
more than one outgoing arc from state B (fig. 1.13(b)) contains the same label
(o), they are not distinct and the transition graph is non-deterministic.
Z