CS 340, Fall 2016 Sep 29th Exam 1 Note: in all questions, the special symbol ɛ (epsilon) is used to indicate the empty string.

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1 CS 340, Fll 2016 Sep 29th Exm 1 Nme: Note: in ll questions, the speil symol ɛ (epsilon) is used to indite the empty string. Question 1. [10 points] Speify regulr expression tht genertes the lnguge over the lphet {, } of ll strings tht end in either or. Exmples of strings in the lnguge: Exmples of strings not in the lnguge: ɛ Question 2. [10 points] Speify regulr expression tht genertes the lnguge over the lphet {, } of ll strings with n even numer of s. Exmples of strings in the lnguge: ɛ Exmples of strings not in the lnguge:

2 Question 3. [10 points] Crete deterministi finite utomton (DFA) tht reognizes the lnguge desried in Question 1. (See tht question for exmples of strings in the lnguge nd not in the lnguge.) Mke sure you indite the strt stte nd the finl stte(s), nd tht eh trnsition hs diretion nd is leled with extly one input symol. Question 4. [10 points] Consider the following two DFAs: q1 q0 q2 q0 q1 Show finite utomton tht reognizes the union of the lnguges reognized y these two utomt. In other words, ny string tht is epted y either of the utomt should e epted, nd ny string tht is rejeted y oth utomt should e rejeted. Hint: your utomton does not need to e deterministi.

3 Question 5. [10 points] Consider the following nondeterministi finite utomton (NFA): ε ε 6 ε 4 5 Convert this NFA into deterministi finite utomton (DFA). Show the tle mpping eh rehle set of NFA sttes to n equivlent DFA stte. Mke sure your DFA indites the strt stte, finl stte(s), nd tht eh trnsition indites diretion nd is leled with extly one input symol.

4 Question 6. [10 points] Crete ontext-free grmmr (CFG) for the lnguge of ALists. The terminl symols re ( ),. An AList is pir of lned prentheses ontining ommseprted list of one or more AItems. Eh AItem is either the terminl symol or n AList. Exmples of strings in the lnguge: ( ) (, ) (, ( ) ) ( ( ) ) ( (, (, ) ), ( ) ) Exmples of strings not in the lnguge: ɛ ( ) ( ( ) ( ) Mke sure to indite wht the strt symol of your grmmr is.

5 Question 7. [20 points] Consider the following ontext free grmmr with the terminl symols nd the nonterminl symol E, whih is the strt symol: E E E 1 E 2 E E E + E E E - () Show derivtion of the input string (Continue on the right-hnd side if neessry.) E String Prodution String Prodution () Drw the prse tree for the derivtion you found in prt ().

6 Question 8. [10 points] Consider the following produtions on the nonterminl symol G: G P G Q G Assume tht,, nd re terminl symols nd G, P, nd Q re nonterminl symols. Show the pseudo-ode for reursive desent prse funtion for the nonterminl G (i.e., prseg funtion). Importnt: Show how to use the lexil nlyzer to hoose etween the possile produtions. Also, show how to rise n error if no prodution n e pplied.

7 Question 9. [10 points] Design Turing Mhine tht tkes string of nd symols s input, nd epts the input (y hlting) if nd only if there re more ourrenes of thn ourrenes of. For exmple, the strings nd would e epted, ut the strings nd would e rejeted. () Strt y stting in words how you ould mke suh Turing Mhine work. () Show the sttes nd trnsitions of the tul Turing Mhine. (Do s muh s you n; sustntil prtil redit will e wrded if you re on the right trk.)

CS 340, Fall 2014 Dec 11 th /13 th Final Exam Note: in all questions, the special symbol ɛ (epsilon) is used to indicate the empty string.

CS 340, Fall 2014 Dec 11 th /13 th Final Exam Note: in all questions, the special symbol ɛ (epsilon) is used to indicate the empty string. CS 340, Fll 2014 Dec 11 th /13 th Finl Exm Nme: Note: in ll questions, the specil symol ɛ (epsilon) is used to indicte the empty string. Question 1. [5 points] Consider the following regulr expression;