Intelligence. Intelligence and Intelligence Testing Module 28.
Intelligence Artificial Intelligence Ian Gent [email protected] Search: 1.
-
Upload
alaina-harlow -
Category
Documents
-
view
218 -
download
0
Transcript of Intelligence Artificial Intelligence Ian Gent [email protected] Search: 1.
Artificial IntelligenceIntelligence
Search: 1
Artificial IntelligenceIntelligence
Part I : What is Search?Part II: Presenting search abstractlyPart III: Basic search algorithms
Search: 1
3
What is AI?
Very hard to define Artificial Intelligence not attempt at building machine to pass Turing Test
Perhaps, exploiting power of machines to do tasks normally considered intelligence?
Practical day to day answer is:AI is what we don’t know how to do yet
Once we know how to do something, it’s not AI e.g. optical character recognition, speech recognition Many AI problems involve combinatorial search
4
Example Search Problem: SAT
We need to define problems and solutionsPropositional Satisfiability (SAT)
really a logical problem -- I’ll present as a letters game
Problem is a list of words contains upper and lower case letters (order unimportant) e.g. ABC, ABc, AbC, Abc, aBC, abC, abc
Solution is choice of upper/lower case letter one choice per letter each word to contain at least one of our choices e.g. AbC is unique solution to above problem.
5
Why is SAT a search problem?
There is no efficient algorithm known for SAT all complete algorithms are exponential time
3-SAT is NP-Complete 3-SAT = each word contains exactly 3 letters
NP-Complete we can recognise solutions in polynomial time
easy to check letter choice satisfies each word all other NP problems can be solved by translation to SAT
Many AI problems fall into NP-Complete class
6
Example: Travelling Salesperson
Problem: graph with an cost for each edge e.g.
Solution: tour visiting all nodes returning to base meeting some cost limit (or reaching minimum cost) e.g. minimum cost is 21 above
TSP is NP-Complete easy to check that tour costs no more than limit (finding optimal cost in technically different complexity class)
4
23
4
5
2
1
42
7
Example (Not): Sorting
Problem, a list of numbers e.g. 5 6 3 2 4 8
Solution, list in ascending order e.g. 2 3 4 5 6 8
In NP (easy to check that result in ascending order)Not NP-complete
cannot solve SAT via sorting can be solved in O(n log n) time
We know how to do it efficiently, so it’s not AI
8
Final Example: Games
Problem: a position in a Chess/Go/… gameSolution: a strategy to guarantee winning gameHarder than NP problems
it is not easy to check that a strategy wins can solve SAT via games
Technically, games usually PSPACE-complete All NP-complete problems in PSPACE
Games are valid AI applicationAI usually attacks NP-complete or harder search
problems
9
Presenting Search Abstractly
Helps to understand the abstract nature of search search states, search spaces, search trees… know what particular search algorithms are trying to do
There are two kinds of search algorithm Complete
guaranteed to find solution or prove there is none Incomplete
may not find a solution even when it existsoften more efficient (or there would be no point)e.g. Genetic Algorithms
For now concerned with complete algorithms
10
Search States
Search states summarises the state of search A solution tells us everything we need to know
e.g. in SAT, whether each letter is UPPER or lower case in TSP, route taken round nodes of graph
This is a (special) example of a search state it contains complete information it solves the problem
In general a search state may not do either of those it may not specify everything about a possible solution it may not solve the problem or extend to a solution
11
Search States
Search states summarise the state of search E.g. in SAT
a search state might be represented by aB
E.g. in TSP a search state might specify some of the order of visits
E.g. in Chess a search state might be represented by the board position
(quiz for chessplayers: …and what else?)
12
Generalising Search
With search states we can generalise search not just finding a solution to a problem
Generally, find a solution which extends search state e.g. find solution to ABC, ABc, AbC, Abc, aBC, abC, abc
which extends aB there is no such solution though whole problem solvable
Original search problem is to extend null stateSearch in AI by structured exploration of search
states
13
Search Space and Search Trees
Search space is logical space composed of nodes are search states links are all legal connections between search states
e.g. in chess, no link between states where W castles having previously moved K.
always just an abstraction think of search algorithms trying to navigate this extremely
complex space
14
Search Trees
Search trees do not summarise all possible searches instead an abstraction of one
possible search Root is null state edges represent one choice
e.g. to set value of A first
child nodes represent extensions children give all possible choices
leaf nodes are solutions/failures Example in SAT
algorithm detects failure early need not pick same variables
everywhere
B(a B )
Im p oss ib le
b(a b )
Im p oss ib le
a(a )
C h oose B
B(A B C )
Im p oss ib le
b(A b C )
S o lu tion
C(A C )
C h oose B
cA c
im p oss ib le
A(A )
C h oose C
A B C , A B c , A b C , A b c , aB C , ab C , ab cs ta te = ()C h oose A
15
Why are search trees abstract?
Search trees are very useful concept but as an abstraction
Search algorithms do not store whole search trees that would need exponential space we can discard nodes in search tree already explored
Search algorithms store frontier of search I.e. nodes in search tree with some unexplored children
Very many search algorithms understandable in terms of search trees and specifically how they explore the frontier
16
Some classic search algorithms
Depth-first search I.e. explore all nodes in subtree of current node before any
other nodes pick leftmost and deepest element of frontier
Breadth-first search explore all nodes at one height in tree before any other
nodes pick shallowest and leftmost element of frontier
Best-first search pick whichever element of frontier seems most promising
17
More classic search algorithms
Depth-bounded depth first search like depth first but set limit on depth of search in tree
Iterative Deepening search use depth-bounded search but iteratively increase limit
18
Next week on Search in AI
Presentation of search algorithms in terms of lists e.g. depth-first = stack, breadth-first = queue
Heuristics in search how to pick which variable to set