Algorithm算法代写代考

5. Weighted FSAs 1 Reminder/summary: (Boolean) FSAs Generation of strings is fundamentally defined like this: (1) x1x2…xn ∈L(M) ⇐⇒ 􏰈 􏰈 ··· 􏰈 􏰉I(q0)∧∆(q0,x1,q1)∧···∧∆(qn−1,xn,qn)∧F(qn)􏰊 q0∈Q q1∈Q qn∈Q Forward and backward are useful “helper functions” whose values can be computed recursively: (2) (3) We (4) (5) (6) fwdM (ε)(q) = I(q) fwdM(x1…xn)(q)= 􏰈 􏰉fwdM(x1…xn−1)(qn−1)∧∆(qn−1,xn,q)􏰊 qn−1 ∈Q

3. Introducing finite-state automata First some standard stage-setting definitions: (1) For any set Σ, we define Σ∗ as the smallest set such that: • ε∈Σ∗,and • ifx∈Σandu∈Σ∗ then(x:u)∈Σ∗. We often call Σ an alphabet, call the members of Σ symbols, and call the members of Σ∗ strings. (2) Foranytwostringsu∈Σ∗ andv∈Σ∗,wedefineu+vasfollows: • ε+v=v • (x:w)+v=x:(w+v) Although

6. Context-free grammars A canonical first example of a context-free grammar (CFG) is shown in (1). This grammar generates the stringset {anbn | n ≥ 1}, i.e. the stringset {ab, aabb, aaabbb, aaaabbbb, . . . }. (1) S → aSb S → ab The fact that the grammar in (1) generates the string ‘aaaabbbb’

CS 561a: Introduction to Artificial Intelligence CS 561, Sessions 6-7 1 This time: Outline Game playing The minimax algorithm Resource limitations alpha-beta pruning Elements of chance CS 561, Sessions 6-7 2 What kind of games? Abstraction: To describe a game we must capture every relevant aspect of the game. Such as: Chess Tic-tac-toe … Accessible