14666_2. problems, problem space n search(lecture 6-11)
TRANSCRIPT
Problems, Problem Spaces and
Search
Chandra Prakash
Assistant Professor
LPU
Contents
Defining the problem as a State Space Search
Production Systems
Control Strategies
Breadth First Search
Depth First Search
Heuristic Search
Problem Characteristics
Is the Problem Decomposable?
Can Solution Steps be ignored or undone?
Production system characteristics
Issues in the design of search programs
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Intelligent Agent
Agent
Environment
State Reward Action
Policy
Agent: Intelligent programs
Environment: External condition
Policy:Defines the agent’s behavior at a given timeA mapping from states to actionsLookup tables or simple function
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Intelligent Agent –Simple Reflex
Intelligent agent (IA) is an autonomous entity which observes and acts upon an environment (i.e. it is an agent) and directs its activity towards achieving goals.
Sensors: to receive stimuli
Actuators: to react
Intelligent agents may also learn or use knowledge to achieve their goals
The goal of artificial intelligence:
To build agents that behave intelligently
Representing states
At any moment, the relevant world is represented as a state
Initial (start) state: S
An action (or an operation) changes the current state to another
state (if it is applied): state transition
An action can be taken (applicable) only if the its precondition is
met by the current state
For a given state, there might be more than one applicable actions
Goal state: a state satisfies the goal description or passes the goal
test
Dead-end state: a non-goal state to which no action is applicable
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Building Goal-Based Agents
We have a goal to reach
Driving from point A to point B
Put 8 queens on a chess board such that no one attacks another
We have information about where we are now at the beginning
We have a set of actions we can take to move around (change from
where we are)
Objective: find a sequence of legal actions which will bring us from
the start point to a goal
Requires defining a “goal test” so that we know what it means to have
achieved/satisfied our goal.
This is a hard part that is rarely tackled in AI, usually assuming
that the system designer or user will specify the goal to be
achieved.
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Problem Representation in AI
Before a solution can be found, the prime condition
is that the problem must be very precisely
defined. The most common methods of problem
representation in AI are:
1. State Space representation
2. Problem Reduction
State Space Representaion:
Are highly beneficial in AI because they provide all
possible state, operations and the goals.
If the entire state-space representation for a problem is
given, it is possible to trace the path from the initial
state to the goal state and identify the sequence of
operations necessary for doing it.
The major deficiency of this method is that it is not
possible to visualize all states for a given problem.
Defining the problem as State Space
Search
Representing states
State space:
Includes the initial state S and all other states that are reachable from S by a sequence of actions
A state space can be organized as a graph:
nodes: states in the space
arcs: actions/operations
The size of a problem is usually described in terms of the number of states (or the size of the state space) that are possible.
Tic-Tac-Toe has about 3^9 states.
Checkers has about 10^40 states.
Chess has about 10^120 states in a typical game.
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Formalizing Search in a State Space• A state space is a graph, (V, E) where V -> set of nodes and E ->set of arcs
• Each arc is directed from a node to another node
• node: corresponds to a state
– state description
– plus optionally other information related to the parent of the node, operation to generate the node from that parent, and other bookkeeping data
• arc: corresponds to an applicable action/operation.
– the source and destination nodes are called as parent (immediate predecessor) and child (immediate successor) nodes with respect to each other
– ancestors( (predecessors) and descendents (successors)
– each arc has a fixed, non-negative cost associated with it, corresponding to the cost of the action
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Cont…
• node generation: making explicit a node by applying an action to
another node which has been made explicit
• node expansion: generate all children of an explicit node by applying
all applicable operations to that node
• One or more nodes are designated as start nodes
• A goal test predicate is applied to a node to determine if its associated
state is a goal state
• A solution is a sequence of operations that is associated with a path in a
state space from a start node to a goal node
• The cost of a solution is the sum of the arc costs on the solution path
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Problem Solving
Problem Solving is a process or procedure used to
find out the solution to a specific problem. To build a
system to solve a particular problem we need to do 4
things.
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To build a system to solve a problem
1. Define the problem precisely
2. Analyze the problem
3. Isolate and represent the task knowledge that is
necessary to solve the problem
4. Choose the best problem-solving techniques and
apply it to the particular problem.
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Problem Solving- steps
1. Define the problem precisely
This definition must include precise
specifications of what the initial situations will be
as well as what the final situations constitute
acceptable solution to the problem.
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Problem Solving - steps
2. Analyze the Problem
A few important features of the problem can help in
the selection of various possible techniques for
solving the problem.
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Problem Solving - steps
3. Knowledge Representation.
Isolate and represent the knowledge that is
necessary to solve the problem.
4. Best Techniques.
Choose the best problem solving technique and
apply it to the particular problem.
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State Space Representation
State Space Representation is a structuredrepresentation of an unstructured problem. It consistsof
1. Initial States
2. Final States (Goal State)
3. Intermediate states
4. Operators, which indicates action to be performed for makingthe changes in the initial states to reach the goal state.
5. A complete knowledge of the problem which is needed forapplying the operators to make a state change.
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Search Through State-Space
Solution Stages
1. Assumptions
2. Solution steps
3. State Space Representations
Initial state
Final state
Operators that can be applied
Abbreviations
State space representation of the given problem
Operators and Conditions.
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State Space Search Example: Water Jug
Problem
Define the Problem Accurately.
“You are given two jugs, a 4 gallon one and a 3
gallon one. Neither has any measuring markers on
it. There is a pump that can be used to fill the jugs
with water. Discuss how exactly 2 gallon of water
can be filled into 4 gallon of jug by employing the
state space representations.
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1. Assumptions
In order to solve the given problem we can make the
following assumptions without affecting the problem.
1. We can fill the jugs with the help of a pump.
2. We can pour water from any jug to the ground.
3. We can transfer water from one jug to the other.
4. No external measuring devices are available.
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2. Solution Steps
We can list the steps that may be followed to reach the goalstate.
1. Fill the 3 gallon jug with water
2. Pour the water from 3 gallon jug to 4 gallon jug.
3. Again fill the 3 gallon jug with water
4. Pour the water carefully from 3 gallon jug to 4 gallon jug such that it is just filled.
5. Empty the 4 gallon jug
6. Transfer the water from 3 gallon jug to 4 gallon jug.
7. Stop.
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State Space Representation
1. Initial & Final States
Let the Quantity of the water present in the jug
represent the state.
State = (Water in 4 G jug, Water in 3 G jug)
Initial State = (0 , 0)
Final State = (2 , n)
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Water Jug Problem
The state space for this problem can be described as the set of ordered pairs of integers (x,y) such that x = 0, 1,2, 3 or 4 and y = 0,1,2 or 3; x represents the number of gallons of water in the 4-gallon jug and y represents the quantity of water in 3-gallon jug
The start state is (0,0)
The goal state is (2,n) for any n.
Attempting to end up in a goal state.
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State Space Representation 2.Operators
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Let us define the following 4 operators.
FILL (jug): where jug = 3 gallon or 4 gallon, fill the
jug fully with water.
EMPTY (jug): where jug = 3 gallon or 4 gallon,
empty the jug by pouring the water to ground.
POUR (jug1, jug2): pour the water from jug1 to
jug 2 until it is just filled
TRANSFER (jug1, jug2): pour the water from jug1
to jug 2 completely.
State Space Representation 3. Abbreviations
G3 3 Gallon Jug
G4 4 Gallon Jug
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4.State Space Representation
State No. Operator State
(G4,G3)
0 (Initial) --------- (0, 0)
1 FILL (G3) (0, 3)
2 TRANSFER (G3, G4) (3, 0)
3 FILL (G3) (3, 3)
4 POUR (G3, G4) (4, 2)
5 EMPTY (G4) (0, 2)
6 (Final) TRANSFER (G3,G4) (2, 0)
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State Space Representation 5.Operators and Conditions
Operators
FILL (G3) :
FILL (G4) :
EMPTY (G4) :
TRANSFER (G3,G4) :
POUR (G3, G4) :
Conditions
G3 was not full
G4 was not full
G4 was not empty
G3 was not empty
& G4 was not full
G3 was not empty
& G4 was not full
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Production rules for Water Jug Problem
The operators to be used to solve the problem can be described as
follows:
Sl No Current state Next State Descritpion
1 (x,y) if x < 4 (4,y) Fill the 4 gallon jug
2 (x,y) if y <3 (x,3) Fill the 3 gallon jug
3 (x,y) if x > 0 (x-d, y) Pour some water out of the 4
gallon jug
4 (x,y) if y > 0 (x, y-d) Pour some water out of the 3-
gallon jug
5 (x,y) if x>0 (0, y) Empty the 4 gallon jug
6 (x,y) if y >0 (x,0) Empty the 3 gallon jug on the
ground
7 (x,y) if x+y >= 4 and y >0 (4, y-(4-x)) Pour water from the 3 –
gallon jug into the 4 –gallon
jug until the 4-gallon jug is
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Production rules
8 (x, y) if x+y >= 3 and x>0 (x-(3-y), 3) Pour water from the 4-gallon
jug into the 3-gallon jug until
the 3-gallon jug is full
9 (x, y) if x+y <=4 and y>0 (x+y, 0) Pour all the water from the 3-
gallon jug into the 4-gallon jug
10 (x, y) if x+y <= 3 and x>0 (0, x+y) Pour all the water from the 4-
gallon jug into the 3-gallon jug
11 (0,2) (2,0) Pour the 2 gallons from 3-
gallon jug into the 4-gallon jug
12 (2,y) (0,y) Empty the 2 gallons in the 4-
gallon jug on the ground
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To solve the water jug problem
Required a control structure that loops through a simple cycle in which some rule whose left side matches the current state is chosen, the appropriate change to the state is made as described in the corresponding right side, and the resulting state is checked to see if it corresponds to goal state.
One solution to the water jug problem
Shortest such sequence will have a impact on the choice of appropriate mechanism to guide the search for solution.
Gallons in the
4-gallon jug
Gallons in the
3-gallon jug
Rule applied
0 0 2
0 3 9
3 0 2
3 3 7
4 2 5 or 12
0 2 9 0r 11
2 0
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Example: Playing Chess
To build a program that could “play chess”, we could
first have to specify the starting position of the chess
board, the rules that define the legal moves, and the
board positions that represent a win for one side or
the other.
In addition, we must make explicit the previously
implicit goal of not only playing the legal game of
chess but also winning the game, if possible
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Playing chess
The starting position can be described as an 8by 8 array where each position contains a symbol for appropriate piece.
Initial position is the game opening position.
Goal position is any position in which the opponent does not
have a legal move and his or her king is under attack.(check
mate position).
The legal moves provide the way of getting from initial state
to a goal state.
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Playing chess (cont…)
Legal moves can be described easily as a set of rules consisting of two parts:
A left side that serves as a pattern to be matched against the current board position.
And a right side that describes the change to be made to reflect the move
However, this approach leads to large number of rules roughly 10120 board positions !!
Using so many rules poses problems such as:
No person could ever supply a complete set of such rules.
No program could easily handle all those rules. Just storing so many rules poses serious difficulties.
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Possible Move
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Defining chess problem as State Space
search We need to write the rules describing the legal moves in as
general a way as possible.
For example:
White pawn at Square( file e, rank 2) AND Square( File e, rank 3) is empty AND Square(file e, rank 4) is empty, then move the pawn from Square( file e, rank 2) to Square( file e, rank 4).
In general, the more accurately we can describe the rules we need, the less work we will have to do to provide them and more efficient the program.
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Formal Description of the problem
1. Define a state space that contains all the possible configurations of the relevant objects.
2. Specify one or more states within that space that describe possible situations from which the problem solving process may start ( initial state)
3. Specify one or more states that would be acceptable as solutions to the problem. ( goal states)
4. Specify a set of rules that describe the actions ( operations) available.
What are unstated assumptions?
How general should the rules be?
How much knowledge for solutions should be in the rules?
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Production Systems
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Production Systems
One of the oldest techniques of knowledge representation.
It is a computer program used to provide some form of AI,
which consists primarily of a set of rules about behavior.
These rules , termed as production are a basic representation.
Production consist of two parts:
Sensory precondition (IF statement)
An action (THEN )
Situation Action
Premise conclusion
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Production System (cont..)
Production System provides structure to AI Program in such a
way that facilities describing and performing the search
process.
Includes a knowledge base,
Represented by production rules,
A working memory to hold the matching patterns of data that
causes the rules to fire and
An interpreter, also called the inference engine, that decides
which rule to fire, when more than one of them are
concurrently firable.
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Production Systems
A production system consists of:
A set of rules, each consisting of a left side(a pattern) that determines the applicability of the rule and a right side that describes the operation to be performed if that rule is applied.
One or more knowledge/databases that contain whatever information is appropriate for the particular task. Some parts of the database may be permanent, while other parts of it may pertain only to the solution of the current problem.
A control strategy that specifies the order in which the rules will be compared to the database and a way of resolving the conflicts that arise when several rules match at once.
A rule applier
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Production system
Inorder to solve a problem:
First reduce it to one for which a precise statement can be given. This can be done by defining the problem’s state space ( start and goal states) and a set of operators for moving that space.
The problem can then be solved by searching for a path through the space from an initial state to a goal state.
The process of solving the problem can usefully be modelled as a production system.
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Control Strategies
If more than one rules is there then how to decide which rule
to apply next during the process of searching for a solution to a
problem?
The three requirements of good control strategy are that
It causes motion:
Otherwise, it will never lead to a solution.
2. It is systematic:
Otherwise, it may use more steps than necessary.
3. It is efficient:
Find a good, but not necessarily the best, answer.
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Breadth-First searchSearching progress level by level generate all the successor of the root node by
applying each as applicable rules to the initial state continue this until we don’t get
goal state
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Breadth First Search
Algorithm:
1. Create a variable called NODE-LIST and set it to initial
state
2. Until a goal state is found or NODE-LIST is empty . do
a. Remove the first element from NODE-LIST and call it E.
If NODE-LIST was empty, quit
b. For each way that each rule can match the state described
in E do:
i. Apply the rule to generate a new state
ii. If the new state is a goal state, quit and return this state
iii. Otherwise, add the new state to the end of NODE-LIST
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BFS Tree for Water Jug problem
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(0,0)
(4,0) (0,3)
(4,3) (0,0) (1,3) (4,3) (0,0) (3,0)
Advantages of BFS
BFS will not get trapped exploring a blind alley.
If there is a solution, BFS is guaranteed to find it.
If there are multiple solutions, then a minimal
solution will be found.
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Amount of time needed to generate all the nodes is
considerable because of the time complexity.
Memory constraint is also a major hurdle because of
the space-complexity.
The searching process remembers all unwanted nodes
which is of no practical use for the search.
Problems Of BFS :
Algorithm: Depth First Search
1. If the initial state is a goal state, quit and return success
2. Otherwise, do the following until success or failure is signaled:
a. Generate a successor, E, of initial state. If there are no more successors, signal failure.
b. Call Depth-First Search, with E as the initial state
c. If success is returned, signal success. Otherwise continue in this loop.
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Backtracking
In this search, we pursue a single branch of the tree until it yields a solution or until a decision to terminate the path is made.
It makes sense to terminate a path if it reaches dead-end, produces a previous state. In such a state backtracking occurs
Chronological Backtracking: Order in which steps are undone depends only on the temporal sequence in which steps were initially made.
Specifically most recent step is always the first to be undone.
This is also simple backtracking.
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Advantages of Depth-First Search
DFS requires less memory since only the nodes
on the current path are stored.
By chance, DFS may find a solution without
examining much of the search space at all.
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The major drawback of DFS is the determination
of the depth until which the search has to
proceed. This depth is called cut-off depth. The
value of cut-off depth is essential because
otherwise the search will go on and on.
If cut-off depth is small, solution may not found
and if cut-off depth is large, time-complexity will
be more.
Drawback of DFS
Traveling Salesman Problem
There are cities and given distances between
them. Travelling salesman has to visit all of them,
but he does not to travel very much. Task is to
find a sequence of cities to minimize travelled
distance.
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Traveling Salesman Problem
A simple motion causing and systematic control structure could solve this problem.
Simply explore all possible paths in the tree and return the shortest path.
If there are N cities, then number of different paths among them is 1.2….(N-1) or (N-1)!
The time to examine single path is proportional to N
So the total time required to perform this search is proportional to N!
For 10 cities, 10! = 3,628,800
This phenomenon is called Combinatorial explosion.
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Branch and Bound
Begin generating complete paths, keeping track of the shortest path found so far.
Give up exploring any path as soon as its partial length becomes greater than the shortest path found so far.
Using this algorithm, we are guaranteed to find the shortest path.
It still requires exponential time.
The time it saves depends on the order in which paths are explored.
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Heuristic Search
A Heuristic is a technique that improves the efficiency of a search process, possibly by sacrificing claims of completeness.
Heuristics are like tour guides
They are good to the extent that they point in generally interesting directions;
They are bad to the extent that they may miss points of interest to particular individuals.
On the average they improve the quality of the paths that are explored.
Using Heuristics, we can hope to get good ( though possibly nonoptimal ) solutions to hard problems such as a TSP in non exponential time.
There are good general purpose heuristics that are useful in a wide variety of problem domains.
Special purpose heuristics exploit domain specific knowledge
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Nearest Neighbour Heuristic
It works by selecting locally superior alternative at each step.
Applying to TSP:
1. Arbitrarily select a starting city
2. To select the next city, look at all cities not yet visited and select the one closest to the current city. Go to next step.
3. Repeat step 2 until all cities have been visited.
– This procedure executes in time proportional to N2
– It is possible to prove an upper bound on the error it incurs. This provides reassurance that one is not paying too high a price in accuracy for speed.
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Heuristic Function
This is a function that maps from problem state descriptions to measures of goal state and usually represented as numbers.
Which aspects of the problem state are considered,
how those aspects are evaluated, and
The weights given to individual aspects are chosen in such a way that
the value of the heuristic function at a given node in the search process gives as good an estimate as possible of whether that node is on the desired path to a solution.
Well designed heuristic functions can play an important part in efficiently guiding a search process toward a solution.
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Example Simple Heuristic functions
Chess : The material advantage of our side over
opponent.
TSP: the sum of distances so far
Tic-Tac-Toe: ???/
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4 square problem :
8 square problem :
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1 3
2 B
B 3
1 2
1 2 3
8 5 6
4 7
1 2 3
8 4
7 6 5
Problem Characteristics
Inorder to choose the most appropriate method for a particular problem, it is necessary to analyze the problem along several key dimensions: Is the problem decomposable into a set of independent smaller or easier
subproblems?
Can solution steps be ignored or at least undone if they prove unwise?
Is the problem’s universe predictable?
Is a good solution to the problem obvious without comparison to all other possible solutions?
Is the desired solution a state of the world or a path to a state?
Is a large amount of knowledge absolutely required to solve the problem or is knowledge important only to constrain the search?
Can a computer that is simply given the problem return the solution or will the solution of the problem require interaction between the computer and a person?
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Is the problem Decomposable?
Whether the problem can be decomposed into
smaller problems?
Using the technique of problem decomposition,
we can often solve very large problems easily.
Example for decomposable problems
∫( x2 +3x + Sin2x.Cos2x )dx
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Blocks World Problem
Following operators
are available:
CLEAR(x) [ block x
has nothing on it]->
ON(x, Table)
CLEAR(x) and
CLEAR(y) ->
ON(x,y) [ put x on y]
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C
A B
A
B
C
Start: ON(C,A)
Goal: ON(B,C) and ON(A,B)
ON(B,C)
ON(B,C) and ON(A,B)
ON(B,C)
ON(A,B)
CLEAR(A) ON(A,B)
CLEAR(A) ON(A,B)
Can Solution Steps be ignored or undone?
Suppose we are trying to prove a math theorem. We can prove a lemma. If we find the lemma is not of any help, we can still continue.
8-puzzle problem
Chess: A move cannot be taken back.
Important classes of problems:
Ignorable (e.g. theorem proving) in which solution steps can be ignored
Recoverable (e.g. 8-puzzle) in which solution steps can be undone.
Irrecoverable (e.g. chess) in which solution steps cannot be undone
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Conti …..
The recoverability of a problem plays an important role in determining the complexity of the control structure necessary for the problem’s solution.
Ignorable problems can be solved using a simple control structure that never backtracks
Recoverable problems can be solved by a slightly more complicated control strategy that does sometimes make mistakes
Irrecoverable problems will need to be solved by systems that expends a great deal of effort making each decision since decision must be final. Planning is required here.
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Is the universe Predictable?
Certain Outcome ( ex: 8-puzzle)
Uncertain Outcome ( ex: Bridge, controlling a robot arm)
For solving certain outcome problems, open loop approach ( without feedback) will work fine.
For uncertain-outcome problems, planning can at best generate a sequence of operators that has a good probability of leading to a solution. We need to allow for a process of plan revision to take place.
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Is a good solution absolute or relative?
Any path problem
Best path problem
Any path problems can often be solved in a reasonable amount of time by using heuristics that suggest good paths to explore.
Best path problems are computationally harder.
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Consider the following problem
1. Marcus was a man
2. Marcus was a Pompean
3. Marcus was born in 40 AD
4. All men are mortal
5. All Pompeans died when volcano erupted in 79 AD
6. No mortal lives longer than 150 years
7. Now it is 1983 AD
“ Is Marcus alive now? “
Is a good solution absolute or relative?
1. Marcus was a man - Axiom1
4. All men are mortal -Axiom4
8. Marcus was Mortal - 1&4
3. Marcus was born in 40 AD -Axiom3
7. Now it is 1983 AD -Axiom7
9. Marcus lived 1983 years - 3,7
6. No mortal lives longer than 150 years Axiom6
10. Marcus is not alive -8,6,9
7. It is now 1983 A.D. Axiom 7
5. All Pompeans died when volcano
erupted in 79 AD Axiom 5
11. All pompeians are dead now 7, 5
2. Marcus was a Pompean Axiom 2
12. So Marcus is not alive 11,2
Is the solution a state or a path?
Examples:
Finding a consistent interpretation for the sentence “The
bank president ate a dish of pasta salad with the fork”. We
need to find the interpretation but not the record of the
processing.
Water jug : Here it is not sufficient to report that we have
solved , but the path that we found to the state (2,0). Thus
the a statement of a solution to this problem must be a
sequence of operations ( Plan) that produces the final state.
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What is the role of knowledge?
Two examples:
Chess: Knowledge is required to constrain the search for a solution
Newspaper story understanding: Lot of knowledge is required even to be able to recognize a solution.
Consider a problem of scanning daily newspapers to decide which are supporting the democrats and which are supporting the republicans in some election. We need lots of knowledge to answer such questions as:
The names of the candidates in each party
The facts that if the major thing you want to see done is have taxes lowered, you are probably supporting the republicans
The fact that if the major thing you want to see done is improved education for minority students, you are probably supporting the democrats.
etc
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Does the task require Interaction with a person?
The programs require intermediate interaction with people for additional inputs and to provided reassurance to the user.
There are two types of programs:
Solitary
Conversational:
Decision on using one of these approaches will be important in the choice of problem solving method.
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Problem Classification
There are several broad classes into which the
problems fall. These classes can each be
associated with generic control strategy that is
appropriate for solving the problems:
Classification : ex: medical diagnostics, diagnosis of
faults in mechanical devices
Propose and Refine: ex: design and planning
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Production System Characteristics
1. Can production systems, like problems, be described by a set of characteristics that shed some light on how they can easily be implemented?
2. If so, what relationships are there between problem types and the types of production systems best suited to solving the problems?
Classes of Production systems:
Monotonic Production System: the application of a rule never prevents the later application of another rule that could also have been applied at the time the first rule was selected.
Non-Monotonic Production system
Partially commutative Production system: property that if application of a particular sequence of rules transforms state x to state y, then permutation of those rules allowable, also transforms state x into state y.
Commutative Production system
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Monotonic Production Systems
Production system in which the application of a
rule never prevents the later application of another
rule that could also have been applied at the time
the first rule was applied.
i.e., rules are independent.
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Commutative Production system
A partially Commutative production system has a property that if the application of a particular sequence of rules transform state x into state y, then any permutation of those rules that is allowable, also transforms state x into state y.
A Commutative production system is a production system that is both monotonic and partially commutative.
79Chandra Prakash, LPU
Partially Commutative, Monotonic
These production systems are useful for solving ignorable problems.
Example: Theorem Proving
They can be implemented without the ability to backtrack to previous states when it is discovered that an incorrect path has been followed.
This often results in a considerable increase in efficiency, particularly because since the database will never have to be restored, It is not necessary to keep track of where in the search process every change was made.
They are good for problems where things do not change; new things get created.
80Chandra Prakash, LPU
Non Monotonic, Partially Commutative
Useful for problems in which changes occur but can
be reversed and in which order of operations is not
critical.
Example: Robot Navigation, 8-puzzle, blocks world
Suppose the robot has the following ops: go North
(N), go East (E), go South (S), go West (W). To reach
its goal, it does not matter whether the robot executes
the N-N-E or N-E-N.
81Chandra Prakash, LPU
Not partially Commutative
Problems in which irreversible change occurs
Example: chemical synthesis
The ops can be :Add chemical x to the pot, Change the temperature to t degrees.
These ops may cause irreversible changes to the potion being brewed.
The order in which they are performed can be very important in determining the final output.
(X+y) +z is not the same as (z+y) +x
Non partially commutative production systems are less likely to produce the same node many times in search process.
When dealing with ones that describe irreversible processes, it is partially important to make correct decisions the first time, although if the universe is predictable, planning can be used to make that less important.
82Chandra Prakash, LPU
Four Categories of Production System
Monotonic NonMonotonic
Partially
Commutative
Theorem
proving
Robot
Navigation
Not Partially
Commutative
Chemical
Synthesis
Bridge
Chandra Prakash, LPU 83
Issues in the design of search programs
The direction in which to conduct the search (
forward versus backward reasoning).
How to select applicable rules ( Matching)
How to represent each node of the search process (
knowledge representation problem)
84Chandra Prakash, LPU
Summary
Four steps for designing a program to solve a
problem:
1. Define the problem precisely
2. Analyse the problem
3. Identify and represent the knowledge required by the
task
4. Choose one or more techniques for problem solving
and apply those techniques to the problem.
85Chandra Prakash, LPU
Reference
Artificial Intelligence by Elaine Rich & Kevin
Knight, Third Ed, Tata McGraw Hill
Artificial Intelligence and Expert System by
Patterson
86Chandra Prakash, LPU