Question: langrage. If it does not exist, a combterexample is rrquirul 3. (10 pts) Let Y={a,b}. Give a DFA/RE, CFG/PDA, and a Tuntz machine that decidies

langrage. If it does not exist, a combterexample is rrquirul 3. (10 pts) Let Y={a,b}. Give a DFA/RE, CFG/PDA, and a Tuntz machine that decidies the language L={w is contains exacly three a's or at lewt oxe b}. if it exists. If any of the three does not exist, prowe in detail why it does not exist. Is LDEC ? ls LP ? 4. (10pts) Lot ={a,b,c,d} Give a DFA/RE, CFG/PDA, and a Turns machine that decides the language L={anbncdkn,k0}, if it ecosta If any of the three does not exist, prove in detail why it doon het eatel Is LDEC ? Is LP ? 5. (10 pts.) Let ={a,b}. Give a DFA/RE, CFG/PDA, and a Turits machine that decides the language L={1www{a,b}}, if it extits If any of the three does not exist, prove in detail why it does not exist Is LDEC ? Is LP ? 6. (10 pts.) Let ={a}. Give a DFA/RE, CFG/PDA, and a Tinins machine that decides the language L=(a2n). if it exists, If any of the three does notexist. prove in detail why it does not exist. Is L DEC" Is LP ? 7. (10 pts.) Use the CYK (dynamic programming) algorithim towwww mine if the following G(SaYZ,ZZYa,YbZZYY) 8. (10pts.) Show that EQDFAP

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