week1 - Week 1 Lecture 1 1 Languages Machines Functions 2...

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Week 1: Lecture 1 1. Languages, Machines, Functions 2. Languages Regular Languages, Context Free Language Context Sensitive Languages Recursively Enumerable Languages How to define? Grammars: Regular Grammars, CFG, CSG etc. Grammar G = (V, Σ , P, S), where V is a finite set called the variables Σ is a finite set, disjoint from V, called the variables P is a set of productions (rules), where each production has a form of α -> β and α , β (V Σ ) * S is the start symbol. Regular grammar CFG, … Example: Even parity strings ({S, A}, {0,1}, P, S), where P is: S -> 1A , S -> 0S, S -> 0 A -> 0A, A -> 1, A -> 1S 3. Machines: Computability Finite State Automata (DFA) M = (Q, Σ , δ , q0, F), where Q: a finite set called states Σ : a finite set called the alphabet δ : Q × Σ Q is the transition function q0 Q is the start state F Q is the set of accept states Example: Even parity language M1 = (Q, Σ , δ , q0, F), where Q = {q0, q1} Σ = {0,1} δ : 0 1 q0 q0 q1 q1 q1 q0
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F = {q0} Example: Language consisting of all strings over {0,1} containing a 0 in the last third position from the end L = {(0+1)* 0 (0+1)(0+1)(0+1) } M1 = (Q, Σ , δ , q0, F), where Q = {q0, q1, q2, q3} Σ = {a,b,c} δ :
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