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### States and Search

Core of intelligent behaviour

The simple problem solver

Restricted form of general agent: Figure 3.1 , p.61

function Simple-Problem-Solving-Agent( percept) returns action

seq an action sequence, initially empty

state some description of the current world state

goal a goal, initially null

problem a problem formulation

state = Update-State(state, percept)

if seq is empty (ie – do search first time only)

goal = Formulate-Goal(state)

if (state==goal) return nil

problem = Formulate-Problem(state, goal) (performance)

seq = Search(problem)

action First(seq)

seq = Rest(seq)

return action

Creating a solution sequence by graph search

D Goforth - COSC 4117, fall 2006

The simple problem solver

- works by simulating the problem in internal representation and trying plans till a good one is discovered
- works in deterministic, static, single agent environments
- plan is made once and never changed
- works if plan is perfect – actions do what plan assumes no corrections to path are required
- works efficiently if space is not too large

D Goforth - COSC 4117, fall 2006

Representation of Environment – abstractions of real world

- states and state space – only relevant information in state representation
- actions - successor function costs
- and path cost (eg touring problem TSP)
- start state
- goal

state or criterion function of state(s)

D Goforth - COSC 4117, fall 2006

Representation of Environment – state space efficiency

Faster processing

- minimization of number of states
- minimization of degree of branching of successor function (actions)

Smaller memory allocation

- large state spaces are generated/explored, not stored/traversed

D Goforth - COSC 4117, fall 2006

Searching state space

The fundamental method

for creating a plan

Is

SEARCH

D Goforth - COSC 4117, fall 2006

Searching – graph traversals – TREE-SEARCH – p. 70

- start node and all possible actions, then pick another node...:

D Goforth - COSC 4117, fall 2006

Design of a search space – the spanning tree over a state space

- Node in search space
- current state
- reference to parent node on path
- action from parent to node
- path cost from start node (may be just path length)

D Goforth - COSC 4117, fall 2006

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Problem-solving agent – exampleNode in search space

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State

Parent link

Action

Path length

D Goforth - COSC 4117, fall 2006

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Problem-solving agent – exampleSPANNING TREE

Note why some state space edges are not traversed in the spanning tree

D Goforth - COSC 4117, fall 2006

General search algorithm – p.72

- EXAMPLE: breadth first search in a binary tree

start state (visitedList)

fringe (openList)

current state

D Goforth - COSC 4117, fall 2006

general search algorithm -variation

startState

initial state of environment

adjacentNode, node

nodes of search tree: contain state, parent, action, path cost

openList

collection of Nodes generated, not tested yet (fringe)

visitedList

collection of Nodes already tested and not the goal

action[n]

list of actions that can be taken by agent

goalStateFound(state) returns boolean

evaluate a state as goal

precondition(state, action) returns boolean

test a state for action

apply(node,action) returns node

apply action to get next state node

makeSequence(node) returns sequence of actions

generate plan as sequence of actions

general search algorithm -variation

algorithm search (startState, goalStateFound())

returns action sequence

openList = new NodeCollection(); // stack or queue or...

visitedList = new NodeCollection();

node = new Node(startState, null, null, 0 0);

openList.insert(node)

while ( notEmpty(openList) )

node = openList.get()

if (goalStateFound (node.state) ) // successful search

return makeSequence(node)

for k = 0..n-1

if (precondition(node.state, action[k])==TRUE)

adjacentNode = apply(nextNode,action[k])

if NOT(adjacentNode in openList OR visitedList)

openList.insert(adjacentNode)

visitedList.insert(node)

return null

algorithms of general search

- breadth first
- depth first
- iterative deepening search
- uniform cost search

D Goforth - COSC 4117, fall 2006

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variations on search algorithm- breadth first search
- openList is a queue
- depth first search
- openList is a stack
- (recursive depth first is equivalent)

tradeoffs for bfs:

shortest path vs resources required

State

Parent link

Action

Path length

D Goforth - COSC 4117, fall 2006

comparison of bfs and dfs

- nodes on openList while search is at level k:
- bfs O(nk ) n is branching factor
- dfs O(nk)
- recursive dfs O(k)
- quality of solution path
- bfs always finds path with fewest actions
- dfs may find a longer path before a shorter one

D Goforth - COSC 4117, fall 2006

depth-limited dfs

- use depth first search

with limited path length

eg

dfs(startNode,goalStateFound(),3)

uses dfs but only goes to level 3

D Goforth - COSC 4117, fall 2006

iterated (depth-limited) dfs

- variation on dfs to get best of both
- small openList of dfs
- finds path with fewest actions like bfs
- repeated searching is not a big problem!!!

D Goforth - COSC 4117, fall 2006

iterative deepening dfs

- search algorithm puts depth-limited dfs in a loop:

algorithm search (startState, goalStateFound())

Node node = null

depth = 0

while (node == null)

depth++

node = dfs(startState,goalStateFound(),depth)

return node

D Goforth - COSC 4117, fall 2006

uniform cost search

- find best path when there is an action cost for each edge:
- a path of more edges may be better than a path of fewer edges:
- 12+8+9+4+10 (5 edges) is preferred to 35+18 (2 edges)
- variation on bfs
- openList is a priority queue ordered on path cost from start state

D Goforth - COSC 4117, fall 2006

uniform cost search - example

openList is a priority queue ordered on path cost from start state

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D Goforth - COSC 4117, fall 2006

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variations of the general algorithm

- openList structure
- time of testing for goal state

D Goforth - COSC 4117, fall 2006

(some) problems that complicate search

- perceptions are incomplete representation of state
- dynamic environment – path of actions is not only cause of state change (eg games)

D Goforth - COSC 4117, fall 2006

what kind of problem-reprise

- fully / partly observable

- is state known?

- deterministic / stochastic

- effect of action uncertain?

- sequential / episodic

- plan required/useful?

- static / dynamic

- state changes between action & perception and/or between perception & action

- discrete / continuous

- concurrent or sequential actions on state

- single- / multi-agent

dynamic environment;

possible communication, distributed AI

D Goforth - COSC 4117, fall 2006

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