CMSC 471

Depth Limited Search

A depth first search with a predetermined depth limit. Incomplete if limit is less than depth. Not optimal if limit is greater than depth.

Iterative Deepening Search

A depth limited search that gradually increases the limit. Generates states multiple times.

admissible heuristic

A heuristic that never overestimates the cost to reach the goal.

Consistent Heuristic

A heuristic ℎh is consistent if its value is nondecreasing along a path. Mathematically, a heuristic ℎh is consistent if for every node 𝑛n of a parent node 𝑝p,

Alpha-Beta Pruning

A method for eliminating branches during the search that will not affect the outcome; Minimax with Alpha-Beta pruning always returns the same scores as Minimax would when using the same depth limit; Potentially much faster than minimax

Best-first search

A node is selected for expansion based on an evaluation function 𝑓(𝑛)f(n)

Thinking Rationally

AI is not here yet

Uninformed Search

Algorithms that are given no information about the problem other than its definition.

What are characteristics of Alpha Beta Pruning

Alpha-beta pruning uses recursion and DFS strategy to send back up utility values from the terminal (leaf) nodes Alpha-beta pruning algorithm keeps track of alpha and beta values for the nodes that it visits and uses them to prune the search tree. Alpha is updated at Max nodes and beta is updated at Min nodes

What is one state of representation?

Atomic

Optimality of A* search

A∗ is complete . The tree-search version of A* is optimal if ℎ(𝑛)h(n) is admissible, while the graph-version is optimal if ℎ(𝑛)h(n) is consistent A∗ has a high space complexity. It runs out of memory pretty quickly.

What is the best example of the Thinking Humanly approach in AI?

Cognitive Modeling

Thinking Humanly

Cognitive Science

BFS performance

Complete; optimal if step costs are equal; Not space efficient because you visit every node at every level; O(b^d) Time complexity is O(b^d)

Depth Limited Search performance

Completeness? No, if 𝑙<𝑑l<d 𝑙l: limit, 𝑑d: the depth of the shallowest solution. Optimality? No, if 𝑙>𝑑l>d 𝑙l: limit, 𝑑d: the depth of the shallowest solution.

Iterative Deepening Search Performance

Completeness? Yes, if b is finite. Optimality? Yes, if the path cost is a nondecreasing function of the depth of the node. Time Complexity? 𝑂(𝑏𝑑)O(bd) b: branching factor, d: the depth of the shallowest solution. Space Complexity? 𝑂(𝑏𝑑)O(bd) b: branching factor, d: the depth of the shallowest solution.

The minimax algorithm uses a strategy for a search similar to

DFS

What is the search algorithm that is used in solving constraint search problems?

DFS

optimality

Does the strategy find the optimal solution? Lowest path cost among all solutions.

A* search

Expand the node that has the minimum value of 𝑓(𝑛)f(n) 𝑓(𝑛)=𝑔(𝑛)+ℎ(𝑛)f(n)=g(n)+h(n) 𝑔(𝑛)g(n) the cost from the start state to the current node ℎ(𝑛)h(n) the estimated cost from the current node to the goal

greedy best-first search

Expands the node that is closest to the goal. Incomplete even if finite f(n) = h(n)

What type of state representation is used in CSP?

Factored

"Least Constraining Value" chooses the variable with minimum number of constraints. T/F

False

A* search and Greedy best-first search both use the same evaluation function f(n) T/F

False

Arc COnsistency keeps track of remaining legal values for the unassigned T/F

False

Backtracking guarantees to find a solution for CSP. T/F

False

C_xy is arc-consistent with respect to variable x if for every value in the domain D_x all values in the domain D_y satisfy the binary constraint on the arc (x, y). T/F

False

Gradient descent is an optimization algorithm but is never used in Machine Learning due to its problems. T/F

False

Greedy Best First Search guarantees both completeness and optimality T/F

False

In Alpha-beta pruning algorithm, you initialize Alpha with +infinity and Beta with -infinity T/F

False

Local maximum is a point where no other point in the entire search space may have a higher objective function than that. T/F

False

Minimum Remaining Values (MRV)" chooses the remaining values that are minimum in the variable domain. T/F

False

The space complexity of DFS is O(b^m) - b to the power of m - where b is branching factor and m is the maximum depth of the search tree T/F

False

Unary constraint restricts the value of two variables. T/F

False

You can use adversarial search in a single-player puzzle game such as Sudoku, or Rubik's cube T/F

False

How do you express this statement in First-Order Logic? Choose the best answer only. No person buys an expensive policy.

For all X For all y(Person(x) and Policy(y) and Expensive(y)) implies not Buys(x,y)

How do you express this statement in First Order Logic? All birds except penguin fly.

For all birds x (bird(x) and -penguin(x)) implies fly(x)

How do you express this statement in First Order Logic? Select all that apply. No robot is human.

For all x Robot(x) implies not Human(X) for all x HUman(x) implies not Robot(x) There does not exists x Robot(x) and Human(X)

What are properties that apply to the chess game environment?

Fully observable Deterministic Semi Dynamic (when played with a clock) Discrete

Task Environment Dimensions and Properties

Fully or partially observable Single-agent or multi-agent Deterministic or stochastic Static or dynamic Discrete or continuous Known or unknown Episodic or Sequential

What is NOT a task environment property

Goal-based vs utility based

time complexity

How long does it take to find a solution?

Space Complexity

How much memory is needed to perform the search?

Which of the following statements are true in the context of state representation? Select all that apply

In an atomic representation, each state of the world is indivisible - it has no internal structure. In a factored representation, each state of the world can be split to a fixed set of variables or attributes. Search algorithms like BFS and DFS work with atomic representations.

Constraint Satisfaction Problem

In which we see how treating states as more than just little black boxes leads to the invention of a range of powerful new search methods and a deeper understanding of problem structure and complexity.

Informed Search

Informed methods are given additional information about the goal; Greedy, A* search

Acting Rationally

Intelligent Agents

completeness

Is the algorithm guaranteed to find a solution when there is one?

What does space complexity deal with?

Memory only

DFS Performance

Not complete for tree version Not optimal Time complexity is O(b^m) Space complexity is O(b*m)

Search environment properties

Observable Discrete Known Deterministic

Search agents

One specific kind of agents that uses with atomic representations on discrete environments.

Contraposition example

P implies not Q is equal to Q implies not P

Assumptions of Adversarial Search

Perfect information, i.e. both players have access to complete information about the states. Zero-sum , i.e. the utility values at the end of the game are equal and opposite. The search environment is fully observable and deterministic.

Task Environment Specification PEAS

Performance Measure External Environment Actuators Sensors

Unit Resolution Example

Premise:A or B, not B Conclusion: A

P or F Unsatisfiable, satisfiable or Valid?

Satisfiable

Student did NOT pass the test. /// Passed (Test) is a boolean statement. Unsatisfiable, satisfiable or Valid?

Satisfiable

Student passed the test. /// Passed (Test) is a boolean statement. Unsatisfiable, satisfiable or Valid?

Satisfiable

T and (T and A) Unsatisfiable, satisfiable or Valid?

Satisfiable

Adversarial Search

Searching in the presence of an adversary adds uncertainty, because you don't know what the opponent will do

Types of Agents

Simple reflex agents Model-based reflex agents Goal-based agents Utility-based agents

intelligent agent

Special-purpose knowledge-based information system that accomplishes specific tasks on behalf of its users

What does rationality depend on

The performance measure that defines the criterion of success. The agent's prior knowledge of the environment The actions that the agent can perform The agent's percept sequence to date

How do you express this statement in First Order Logic? Choose the best answer only. Some kids like candy.

There exists x Kid(X) and Likes(x,candy)

A partial assignment is one that assigns values to only some of the variables. T/F

True

A solution must be a complete and consistent assignment. T/F

True

A variable in a CSP is arc-consistent if every value in its domain satisfies the variable's binary constraints. T/F

True

A* usually runs out of space long before it runs out of time. For this reason, A* is not practical for many large-scale problems. T/F

True

An admissible heuristic always underestimates the true cost of getting from a state to the goal state. T/F

True

An assignment that does not violate any constraints is called a consistent or legal assignment T/F

True

An assignment that does not violate any constraints is called a consistent or legal assignment. T/F

True

BFS is complete if the branching factor b is finite T/F

True

Backtracking algorithm is a CSP solver T/F

True

Backtracking has inefficiency issue because it may explore areas of the search space that aren't likely to succeed. T/F

True

Both BFS and DFS are both uninformed search T/F

True

Both versions of DFS (tree-search and graph-search) are non-optimal. T/F

True

C_xy is arc-consistent with respect to variable x if for every value in the domain D_x there is some value in the domain D_y that satisfies the binary constraint on the arc (x, y). T/F

True

Comparing AI, Machine Learning, and Deep Learning, one can argue that there is a superset-subset relationship between them such that Deep Learning is a subset of Machine Learning approaches, and Machine Learning is a subset of the broad field of approaches, algorithms and techniques in AI. T/F

True

Consistency is a stronger condition than admissibility T/F

True

Depth-first tree search needs to store only a single path from the root to a leaf node, along with the remaining unexpected sibling nodes for each node on the path, and that is why DFS has a lower space complexity than BFS. T/F

True

Every consistent heuristic is also admissible. T/F

True

Hill climbing may get stuck in local maximum. T/F

True

Hill climbing may get stuck in plateau - flat area T/F

True

IDA*, Recursive Best First Search (RBFS) and SMA* are memory-bounded heuristic searches that try to overcome the issue with A* space complexity - high memory usage. T/F

True

In Genetic Algorithm, each location in the offspring (after crossover) is subject to random mutation with a small independent probability. T/F

True

Intelligence is concerned with mainly rational action T/F

True

Iterative deepening DFS combines the benefits of DFS and BFS. Its space complexity is O(bm) like DFS and it is complete like BFS if the branching factor is finite. T/F

True

Minimum Remaining Values (MRV), Most Constraining Variable and Least Constraining Value are among the heuristics used to make backtracking more efficient. T/F

True

Most Constraining Variable" chooses the variable involved in largest number of constraints on remaining variables. T/F

True

Random restart is one way to overcome hill climbing failure. T/F

True

Rationality is NOT omniscience. Omniscience is impossible in reality T/F

True

Selection, crossover and mutation are all random processes T/F

True

Simulated annealing sometimes allows for bad moves based on a probability that decreases over time T/F

True

Space complexity of DFS is O(bm) where b is the branching factor and m is the maximum depth of the search tree. T/F

True

Space complexity of DFS is lower than BFS. T/F

True

The interdisciplinary field of Cognitive Science brings together computer models from AI and experimental techniques from psychology to construct precise and testable theories of the human mind. T/F

True

The temperature T decreases over time (cools down) to reduce the probability of bad moves by simulated annealing. T/F

True

The term percept refers to the agent's perceptual inputs at any given instant. T/F

True

The time complexity of BFS is O(b^d) where b is branching factor and d is the depth of the shallowest solution. T/F

True

The tree-search version of A* is optimal if h(n) is admissible, while the graph-search version is optimal if h(n) is consistent. T/F

True

The tree-search version of DFS is not complete even if the branching factor b and the depth d are finite. T/F

True

Using heuristics may detect failure of a path earlier. T/F

True

When a CSP is not arc consistent, we may make it arc consistent by using the AC3 algorithm with no guarantee for all problems. T/F

True

there does not exist and x P(x) = for all X -P(x)

True

Acting Humanly

Turing Test

What is the best example of "Acting Humanly"?

Turing Test

Which of the following is NOT an assumption about the search environment?

Unknown

p and not p Unsatisfiable, satisfiable or Valid?

Unsatisfiable

Informed Search

Uses problem-specific knowledge beyond the definition of the problem itself.

-P or T Unsatisfiable, satisfiable or Valid?

Valid

P--> P Unsatisfiable, satisfiable or Valid?

Valid

Breadth First Search

Visits the neighbor vertices before visiting the child vertices Often used to find the shortest path from one vertex to another. A queue is usually implemented

(P or Q) And R CNF?

Yes

P And Q CNF?

Yes

P or Q CNF?

Yes

percept

a mental concept that is developed as a consequence of the process of perception

Depth First Search

a search in which children of a node are considered (recursively) before siblings are considered.

zero-sum assumption

equal and opposite payoff for each player

heuristic function

estimated cost of the cheapest path from the state at node n to a goal state - this is non-negative and problem specific.

What is the A* evaluation function?

f(n) = g(n) + h(n)

Factored state representation

internal structure, although exactly what will depend on the problem

minimax tree

levels switch from max and min nodes

If h1 and h2 are both admissible heuristics, which of the following heuristics are guaranteed to be admissible.

max(h1, h2) min(h1, h2)

Atomic State representation

qualitative measure of how much "internal structure" those models have, from least to most.

structured state representation

relations either of components of the model to itself, or components of the model to components of the environment.

alpha entails beta if and only if alpha implies beta is valid T/F

true

for all x P(x) - there does not exist x not p(x)

true

not for all X P(x) = there exists x not P(X)

true

there exists P(x) = not for all x not p(x)

true