AI Programming Lecture 6 Problem Reduction

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AI ProgrammingLecture 6Problem Reduction

• Richard Price Simon Worgan
• School Of Computer Science University Of
  Birmingham
• msc59rmp, msc74sxw_at_cs.bham.ac.uk

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Last Week

• Large search spaces.
• Heuristic search.
• Best first search.
• A search.

3
Introduction

• Problem reduction.
• Terminology.
• Simple Example
• STRIPS.
• Blocks World.

4
Problem Reduction

• Finding solutions
• Search
• Is there a solution?
• Planning
• How can I find a solution?
• May require reasoning.
• Sub-goals often make problems easier.
• Like waypoints on a route.
• Divide Conquer.
• Considerations
• Multiple ways to divide a problem.
• Multiple ways to achieve goal(s).

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Terminology

• The root of the tree is the goal.
• Each sub-goal is a node in the tree.
• A rule is the connection between two nodes.
• A rule can only be used if all its conditions are
  satisfied.
• A rule without any sub-goals is a fact.
• A list of rules is a rulebase.

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And/Or-Nodes

• An And-node is a sub-goal that precedes other
  goals.
• An Or-node is a goal with multiple rules.

Goal
Rule
Sub-Goal
And-Node
Or-Node
Fact
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Simple Example

• / Facts /
• ingredients
• money
• / Rules /
• food time ingredients
• food money
• -gt rulebase

food
food time ingredients
food money
money
ingredients
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Searching Backwards

• define backwardsSearch1(goals) -gt bool
• lvars goal, subGoals, otherGoals
• if goals then true -gt bool
• else goals --gt !?goal ??otherGoals
• foreach !goal ??subGoals in rulebase do
• backwardsSearch1(subGoals) -gt bool
• if bool if goal succeeds, then recurse on
  otherGoals
• then backwardsSearch1(otherGoals) -gt bool
• if bool then return endif
• endif
• endforeach
• false -gt bool if nothing succeeded
• endif
• enddefine
• backwardsSearch1(food) -gt bool

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Strategies

• Generally either
• Progressive From initial state to the goal.
• Regressive From goal to initial state.
• Rules can also generate new states.
• Like actions changing the environment.
• The order you perform actions sub-goals forms a
  plan.
• STRIPS is perhaps the most famous planning
  algorithm.

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Planning - STRIPS
Start
Goal

• Actions -gt Updating a database of facts.
• Need to know
• Our initial state
• Our desired state
• How we can change our state

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STRIPS - Representation

• States Goals
• Conjunctions of facts
• e.g CurrentState OnTable(A) OnTable(B)
  OnTop(C, B) Clear(A) Clear(C) HandEmpty
• Can be stored in the POP-11 database

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Representation - Actions

• Description
• pickup(x)
• Required Sub-Goals
• handEmpty Clear(x) (onTable(x) or onTop(x,
  y))
• Effect
• handEmpty holding(x) clear(x)
  (onTable(x) or onTop(x,y))

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The Environment

• Accessible Complete Knowledge
• Deterministic
• Episodic
• Static
• Discrete

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Blocks World

• Fits these criteria

B
A
A
C
B
C
Goal
Initial State
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Regression - Algorithm

• Create Stack
• Push Goal
• While(!(Stack empty))
• Examine top of stack
• If(sub-goal met)
• Pop sub-goal
• If(an action leads to sub-goal)
• Push Action
• Push sub-goals required by Action
• If(an action)
• Pop and Execute Action
• Endwhile

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Search Vs. Planning

• Planning allows for Sub-Goals.
• Divide and Conquer approach.
• Often backwards search (regression) reduces
  branching factor.
• Sequence to initial state does not matter.

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Practical uses of Planning

• Shakey the robot MIT Labs
• OPTIMUM-AIV European Space Agency
• O-PLAN Hitachi
• SPIKE Hubble Space Telescope
• SIPE Skyscraper construction

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Conclusion

• Planning uses sub-goals heavily
• Divide Conquer.
• STRIPS Simple, effective, the use of logical
  actions in goal finding.
• Consider the environment limitations.