Lec-4: What is State Space Search | Introduction to Problem Solving in Artificial Intelligence — Transcript

Full transcript

1. 0:00Hello friends welcome to Gate Smashers
2. 0:02In today's video we are going to discuss
3. 0:05State space searching
4. 0:06It is one of the major application of artificial intelligence
5. 0:09Problem solving
6. 0:10That is how to solve a particular problem
7. 0:12And if we talk about era of 1960-1970
8. 0:15At that time the major research that was done in artificial intelligence
9. 0:19That is done on problem solving
10. 0:22And in which if we talk related to game
11. 0:24Like tic tac toe game is there
12. 0:26Water jug problem, 8 queen problem
13. 0:28Chess game, Go
14. 0:29How can we solve these problems
15. 0:32Through machines
16. 0:33Through agent
17. 0:34As human being solves the problem
18. 0:37In the same way we want that the machine should solve the problem
19. 0:40So that is called a problem solving area
20. 0:43In problem solving area
21. 0:45State space searching is very important
22. 0:48What is the reason
23. 0:50What is it's meaning, what is the meaning of state space over here
24. 0:53Number of states
25. 0:55In which the problem can go
26. 0:57All the different states
27. 0:59If we normally talk on our level also
28. 1:02Let's say if we start research on any topic
29. 1:05If we start research
30. 1:06Then obviously we will not reach at all the places in one time
31. 1:10We start with a start state
32. 1:12We have a goal state
33. 1:14Now it is possible that between start and goal state there are some intermediate state
34. 1:18We go level by level
35. 1:20We achieve our goal state
36. 1:22So all the set of states
37. 1:24We use them in the form of representation
38. 1:27Because in artificial intelligence we majorly talk
39. 1:30How to represent the problem
40. 1:34Precisely
41. 1:35Because representing a problem is a major task
42. 1:38Because if you are giving this problem to your machine or to your agents
43. 1:42Then you cannot tell it verbally
44. 1:45That this is the problem
45. 1:47You see for yourself also
46. 1:48If you start playing any new game
47. 1:50You do not know anything about that game
48. 1:51In your house your elders are playing your brothers and sisters are playing
49. 1:54So obviously you want someone to tell you that how to play that game
50. 1:57Tell me all the rules once
51. 2:00Which are the set of states in it
52. 2:03How will I play it
53. 2:03All these points
54. 2:04It is necessary for you to represent the problem precisely
55. 2:09And other than that
56. 2:12If we will represent it precisely
57. 2:14Then we can also easily analyze it
58. 2:17How we have to play the game
59. 2:19How we can take steps one by one
60. 2:22So to represent the problem precisely
61. 2:25And if you want to represent the problem in all set of states
62. 2:29Then we use the 'state space search'
63. 2:33And over here we use this tupple
64. 2:36In which S represents total number of states
65. 2:39And which are the major states in S
66. 2:42Start state
67. 2:43Goal state
68. 2:44Intermediate states are there
69. 2:47Obviously between start and goal there will be some intermediate states
70. 2:50Then A
71. 2:52A is set of actions
72. 2:54All possible actions
73. 2:55Let's say we take an example
74. 2:588 puzzle problem
75. 3:01If we talk about 8 puzzle problem
76. 3:03So obviously what I want in it first of all
77. 3:05That I tell my machine or agent, the problem very clearly
78. 3:09So what are you telling in 8 puzzle problem
79. 3:11That we have a board of 3 * 3
80. 3:14And we have 9 spaces in board of 3*3
81. 3:18Obviusly the board is of 3*3 so how many places we will have
82. 3:21We will have 9 places
83. 3:23In which we have 8 tiles
84. 3:25Which are numbered
85. 3:26Lets say we have number 2
86. 3:283, 4, 1, 6, 7, 8
87. 3:375
88. 3:38Let's say in this way
89. 3:39Now I have random tiles numberd 1,2,3,4,5,6,7,8
90. 3:43I have numbered tiles
91. 3:45And I have one empty space
92. 3:48Now over here first of all I have to represent the problem precisely
93. 3:52That I have board of 3*3
94. 3:54And these are the plates that I have
95. 3:55Next what we have
96. 3:57I know that this is my start state
97. 4:01Now I want goal state
98. 4:03Where I want to reach
99. 4:04Otherwise you will keep on searching
100. 4:06Obviously somewhere you should know your goal state
101. 4:09So let's say if we define our goal state
102. 4:11That this is my goal state
103. 4:13Then you can easily start your search from goal state
104. 4:18So that you can reach to goal state
105. 4:20Let's say this is my goal state 1,2,3,4,5,6,7,8
106. 4:26This is my goal state
107. 4:28This is my start state
108. 4:29Now when we start searching
109. 4:32When we start exploring it
110. 4:34Then obviously my intermediate states will start forming
111. 4:37So I will compare each intermediate state with this
112. 4:41Whether it is my goal state or not
113. 4:43When I will get, then the searching will stop over there
114. 4:45So this is the basic concept
115. 4:47Of searching
116. 4:47Actions
117. 4:49If we talk about all possible actions
118. 4:51What A? All possible actions
119. 4:52What are all possible actions
120. 4:54That my empty space
121. 4:56Either I can move it upward
122. 4:59I can move it downward
123. 5:00I can move it left
124. 5:02Or I can move it right
125. 5:05These are my 4 possibilities
126. 5:07These are the 4 possibilities I have
127. 5:09You should know about legal and illegal moves
128. 5:12Obviously, you will say that I can take 5 over here, and I will move 2 over here
129. 5:16No
130. 5:17That is a illegal state
131. 5:18So you should know all the rules over here
132. 5:22You will have to predefine them
133. 5:23So over here what am I saying
134. 5:25That the empty space can be replaced by left, right, up or down
135. 5:31Now I will choose any one action from that
136. 5:34I will have to choose any one action
137. 5:36Let's say in this
138. 5:38First of all move upward
139. 5:41So what is the meaning of moving upward
140. 5:43That this my new state
141. 5:45Which you can say it is an intermediate state
142. 5:48In which what I have done
143. 5:49I have moved the space upward
144. 5:51That means 3 came here
145. 5:52Other places are as it is
146. 5:57In this way
147. 5:57What can be the second one
148. 5:59Let's say if I move it downwards
149. 6:01Then I can move it this way
150. 6:03Like this
151. 6:06I will take the space down
152. 6:087 will come up
153. 6:09Rest of the concept is the same
154. 6:115, 1, 8, 6
155. 6:14So this I ahve bought space downward
156. 6:17In the same way if we keep the space on left side
157. 6:19Then this will be formed over here like this
158. 6:25If I do it on left then 5 will come here
159. 6:262,3,4,1,6,7,8
160. 6:31In the same way you can move it to right side
161. 6:34What are doing actually
162. 6:36You are starting to explore your searching
163. 6:40And these are different branches
164. 6:42These different branches are getting formed
165. 6:44Then what you can do ahead in this
166. 6:47Look here carefully
167. 6:48You can either move the space in left
168. 6:51Or you can move it right
169. 6:52Or you can move it down
170. 6:54You cannot move it up
171. 6:55In the same way if we talk over here
172. 6:57You cannot move down
173. 6:58You can go up, left and right
174. 6:59If we talk in this then, you can do up
175. 7:01You can do right and down
176. 7:03But you cannot do left
177. 7:04So this is set of all possible
178. 7:06But from that which one you have chosen
179. 7:08In this which one you have chosen?
180. 7:10You moved upward
181. 7:12So which ever set of action you choose, it will be this Action(s)
182. 7:17Then result
183. 7:18Result means you are reaching on which result
184. 7:21On which resultant state you are reaching
185. 7:23So let's say these all are resultant only
186. 7:26Now after this if you move it left side
187. 7:29Then the next state
188. 7:30That will be one of my resultant state
189. 7:32Then comes cost
190. 7:34We measure it in cost
191. 7:35What is the meaning of cost
192. 7:36Generally we consider that
193. 7:38That I have moved this once on the left side
194. 7:40Then let's say we will take its cost
195. 7:421
196. 7:43Generally in spanning tree we find the distance
197. 7:46Then at the time of distance
198. 7:47We generally use
199. 7:49If I want to go from one place to another place or from one edge to another edge
200. 7:52Or from One node I want to reach to another node
201. 7:55Then how much distance I am covering
202. 7:57That can be time
203. 7:59Anything, we will consider a general constant value
204. 8:01That is called a cost
205. 8:03So obviously we want that our searching
206. 8:06It should be in minimum cost
207. 8:08The obviously that solution
208. 8:11That we will count as best solution
209. 8:14So what benefit you are getting from state based search
210. 8:18One is that you are precisely defining
211. 8:20Your agent can properly analyze that how we can move
212. 8:24And we talk in artificial intelligence
213. 8:27Next important point
214. 8:29That when we start the searching
215. 8:31In any problem
216. 8:33Water jug or 8 queen
217. 8:34Or you consider 8 puzzle
218. 8:3615 puzzle, chess
219. 8:37In any of them
220. 8:38Now we have started exploring this
221. 8:39Ahead of this also state will be formed in this
222. 8:41Further states of this also will be formed
223. 8:43So all the states that are formed
224. 8:45That means you are going on searching
225. 8:47You are searching for goal state
226. 8:48So we do searching in how many ways?
227. 8:51We do searching in 2 ways
228. 8:53Either we do it uninformed
229. 8:55Which we call as blind search
230. 8:57What is the meaning of blind
231. 8:59I don't know anything about the domain about my problem
232. 9:02I just know start and goal
233. 9:03I keep on exploring
234. 9:05And I am matching each state with this
235. 9:08Or we have informed search
236. 9:11In informed search we use concept of heuristic
237. 9:15Due to which we try to solve the problem quickly
238. 9:19In which we go towards benefit towards local benefit
239. 9:23So that my problem can get solved quickly
240. 9:25Because uninformed takes exponential time
241. 9:29Because in uninformed
242. 9:30B^d
243. 9:32Time complexity is O(b^d)
244. 9:34In which b is branching factor
245. 9:36If we talk about this when we started how many branches were formed
246. 9:404 branches will be formed
247. 9:42It is possible after this next there can be 3-4 branches
248. 9:44In the same way the number of branches that are formed
249. 9:47And depth
250. 9:49Depth means till how much depth this will go
251. 9:52Which is it's tree
252. 9:53If we talk over here
253. 9:54What is it's depth 1
254. 9:56Then we explored it ahead
255. 9:57Then over here this is one depth
256. 9:58That means from root till leaf how much depth is going
257. 10:03That is called depth
258. 10:04So in this I will tell you about uninformed over here
259. 10:07Although I have explained uninformed and informed in the next video
260. 10:11Their all the differences
261. 10:12Basically uninformed
262. 10:14Non-polynomial that means it grows exponential time
263. 10:18Like if we talk about this problem
264. 10:21When you will make state spaces
265. 10:23When you will make number of states
266. 10:25Then it can grow upto 3^20 number of states
267. 10:30That means more then 3.5 billion states can be covered
268. 10:34Somewhere for a machine or agent
269. 10:39It is more time consuming to cover so many states
270. 10:42That's why we prefer to
271. 10:44Use informed searching