The document summarizes key topics from a session on artificial intelligence taught by Assistant Professor M. Gokilavani, including adversarial search, constraint satisfaction problems, and propositional logic. It discusses constraint propagation techniques like node consistency and arc consistency to reduce the domains of variables. Backtracking search and local search methods for solving constraint satisfaction problems are described, along with ways to improve backtracking efficiency through variable and value ordering and constraint filtering. The use of problem structure to decompose problems is also covered.

1. ARTIFICAL INTELLIGENCE
(R18 III(II Sem))
Department of computer science and
engineering (AI/ML)
Session 19
by
Asst.Prof.M.Gokilavani
VITS
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2. TEXTBOOK:
• Artificial Intelligence A modern Approach, Third
Edition, Stuart Russell and Peter Norvig, Pearson
Education.
REFERENCES:
• Artificial Intelligence, 3rd Edn, E. Rich and
K.Knight (TMH).
• Artificial Intelligence, 3rd Edn, Patrick Henny
Winston, Pearson Education.
• Artificial Intelligence, Shivani Goel, Pearson
Education.
• Artificial Intelligence and Expert Systems-
Patterson, Pearson Education.
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3. Topics covered in session 19
• Adversarial Search: Games, Optimal Decisions in Games, Alpha–
Beta Pruning, Imperfect Real-Time Decisions.
• Constraint Satisfaction Problems: Defining Constraint
Satisfaction Problems, Constraint Propagation, Backtracking
Search for CSPs, Local Search for CSPs, The Structure of
Problems.
• Propositional Logic: Knowledge-Based Agents, The Wumpus
World, Logic, Propositional Logic, Propositional Theorem
Proving: Inference and proofs, Proof by resolution, Horn clauses
and definite clauses, Forward and backward chaining, Effective
Propositional Model Checking, Agents Based on Propositional
Logic.
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4. Constraint Propagation
• In local state-spaces, the choice is only one,
i.e., to search for a solution. But in CSP, we
have two choices either:
– We can search for a solution or
– We can perform a special type of inference
called constraint propagation.
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5. Constraint Propagation
• Constraint propagation is a special type of inference
which helps in reducing the legal number of values
for the variables.
• The idea behind constraint propagation is local
consistency.
• In local consistency, variables are treated as nodes,
and each binary constraint is treated as an arc in the
given problem.
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6. There are following local consistencies which are
discussed below:
• Node Consistency: A single variable is said to be node
consistent if all the values in the variable’s domain satisfy
the unary constraints on the variables.
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7. • Arc Consistency: A variable is arc consistent if every
value in its domain satisfies the binary constraints of the
variables.
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Path Consistency: When the evaluation of a set of two
variable with respect to a third variable can be extended over
another variable, satisfying all the binary constraints. It is
similar to arc consistency.
k-consistency: This type of consistency is used to define the
notion of stronger forms of propagation. Here, we examine
the k-consistency of the variables.

8. Backtracking Search for CSPs
• In CSP’s, variable assignments are commutative
For example:
[WA = red then NT = green]
is the same as
[NT =green then WA = red]
• We only need to consider assignments to a single
variable at each level (i.e., we fix the order of
assignments)
• Depth-first search for CSPs with single-variable
assignments is called backtracking search.
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9. Example
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10. Example
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11. Example
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12. Example
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13. Example
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14. Backtracking Searching Algorithm
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15. Problem in ordering
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• Ordering
– How should we order variables for assignment?
– How should we order values from the domains?
Need Improving Backtracking Efficiency Ordering

16. Improving Backtracking Efficiency
Ordering
• Ordering
– How should we order variables for assignment? –
– How should we order values from the domains?
Filtering
Can we detect inevitable failures early?
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17. Early detection of failure
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18. Early detection of failure- Forward
Checking
• Forward checking Keep track of remaining legal values
for unassigned variables.
• Terminate search when any variable has no legal values.
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19. Arc Consistency
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20. Arc Consistency
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21. Problem structure
• Tasmania and the mainland are separate structures. We can
solve them independently and then combine their solutions.
• More generally, we can decompose the CSP into separate
connected components (sub-problems of the CSP).
• Then the solution is the union of the sub- problem solutions.
This can be much more efficient than solving the entire CSP
as one problem.
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22. Algorithm for tree structure CSP’s
• Choose one variable as root, order variables from root to
leaves such that every node's parent precedes it in the ordering.
• Backward removal phase: check arc consistency starting
from the rightmost node and going backwards.
• Forward assignment phase: select an element from the
domain of each variable going left to right. We are guaranteed
that there will be a valid assignment because each arc is arc
consistent.
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23. Local search methods
• Improve what you have until you can’t make it better.
• Generally much faster and more memory efficient
than back-tracking search (but not necessarily
complete).
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24. Local search for CSP’s
• Start with an initial assignment of variables to values
• Allow states with unsatisfied constraints
• Attempt to improve states by reassigning variable
values.
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25. Local search for CSP’s
Hill-climbing search:
• In each iteration, randomly select any conflicted variable
and choose value that violates the fewest constraints
• I.e., attempt to greedily minimize total number of violated
constraints h = number of conflicts.
• Problem: local minima h = 1
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26. Hill climbing state space diagram
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27. Topics to be covered in next
session 20
• Propositional Logic
Thank you!!!
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