Hmk1-RegLang

# Hmk1-RegLang - COT 4210(Proof Homework#1 Regular Languages...

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COT 4210 (Proof) Homework #1: Regular Languages Due Date: Thursday September 8, 2011 Note: Unless otherwise noted, assume the alphabet for each language is {0, 1}. 1) Draw the state diagram for the DFA formally described below: {Q, Σ, δ, q 0 , F} where Q = {q 0 , q 1 , q 2 , q 3 , q 4 } Σ = {0, 1} Start state = q 0 F = {q 1 , q 3 } δ = 0 1 q 0 q 0 q 1 q 1 q 4 q 0 q 2 q 3 q 4 q 3 q 0 q 1 q 4 q 2 q 3 2) Draw a DFA that accepts the following language: { w | w’s decimal equivalent is divisible by 6 } 3) Draw a DFA that accepts the following language: { w | w starts with 11 or ends with 00 } 4) Draw an NFA that accepts the following language: { w | w contains either the substring 1101 or 0110 }

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5) Prove that every NFA can be converted to another equivalent NFA that has only one accept state. 6) Your friend Tommy thinks that if he swaps the accept and reject states in an NFA that accepts a language L, that the resulting NFA must accept the language L . Show, by way of counter- example, that Tommy is incorrect. Explain why your counter-example is one.
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Hmk1-RegLang - COT 4210(Proof Homework#1 Regular Languages...

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