R10 SET - 1 0,1 0,1. 3. a) Convert the following finite automata to regular expressions

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1 R0 SET - II B. Tech II Semester Supplementry Exmintions Jn/Fe FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science nd Engineering) Time: 3 hours Mx. Mrks: 75 Answer ny FIVE Questions All Questions crry Equl Mrks ~~~~~~~~~~~~~~~~~~~~~~~~~. ) Define finite stte mchine nd explin model of finite utomton? ) Find the lnguge ccepted y following finite utomton: (9M+6M) 0 2. ) Design Finite Stte Acceptor to ccept the lnguge of ll inry strings tht do not include the sustring 0. ) Design Moore mchine to determine the residue mod 5 for ech inry string treted s integer. 3. ) Convert the following finite utomt to regulr expressions Strt 2 q r s 0, ) Using pumping lemm, show the following lnguge is not regulr: 0, * { w ( 0 + ) the numer of 0's w is perfect squre} L = (0M+5M) of 2, 3 2

2 R0 SET - 4. ) Otin Right Liner Grmmr for the lnguge L = { n m n 2, m 3 } ) Recognize the context free lnguge for the following CFG: S B A A S AA B S BB (6M+9M) 5. ) Wht is Greich Norml Form? Write the procedure to convert CFG into Greich Norml form. ) Convert the following CFG into Chomsky Norml Form: S ABA A A B B * 6. ) Design PDA for the lnguge L { w w ( + ) nd n ( w) > n ( w) } = ) Discuss in detil out different pproches for cceptnce of lnguge y Push down Automt. 7. ) Differentite etween recursive nd recursively enumerle lnguges. ) Give Turing mchine tht shifts the input string, over the lphet {0,} y one position right y inserting #'s the first chrcter. 8. ) Define Post correspondence prolem nd Modified PCP. Wht is the difference etween PCP nd MPCP? ) For given recursively enumerle lnguge, it is undecidle to determine whether it is empty or not. Justify your nswer. 2 of 2

3 R0 SET - 2 II B. Tech II Semester Supplementry Exmintions Jn/Fe FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science nd Engineering) Time: 3 hours Mx. Mrks: 75 Answer ny FIVE Questions All Questions crry Equl Mrks ~~~~~~~~~~~~~~~~~~~~~~~~~. ) Give DFA s ccepting the following lnguges over the lphets{0,}: The set of ll strings eginning with tht,when interpreted s inry integer, is multiple of 5.For exmple, strings 0,00nd re in the lnguge; 0,00 nd re not. ) Define DFA nd NFA. Explin the difference etween them with n exmple. 2. ) For the following NFA with moves convert it into n NFA without moves nd show tht NFA with -moves ccepts the sme lnguge s shown in Figure 2 elow ) Descrie in detil out conversion of Moore to Mely mchine. 3. ) Explin out pumping lemm for regulr sets. ) Give regulr expression for the set of ll strings over {, } ccepting ll strings which hve numer of s divisile y 6 nd numer of s divisile y 8. (6M+9M) of

4 R0 SET ) Show tht id+id*id cn e generted y two distinct left most derivtions in the grmmr E E+E E*E (E) id ) Wht is left liner nd right liner grmmrs? Discuss in detil out conversion from left liner to right liner grmmr. 5. ) Explin pumping lemm for CFL.Consider the following lnguge L={ n n c n n },using pumping lemm show tht L is not CFL. ) Check whether the given grmmr is miguous or not S icts S ictses S C 6. ) Define Push Down Automt nd explin its model with net digrm. ) Construct PDA for the following grmmr: S AB A CD B C D 7. ) Design Turing Mchine tht ccepts the set of ll even plindromes over {0,}. ) Wht is Turing mchine? Wht re vrious types of Turing mchines? Descrie in detil out vrious representtions of Turing mchines. 8. ) Show tht the following post correspondence prolem hs solution nd give the solution. I List A List B ) Discuss in detil out P prolems nd NP prolems. (0M+5M) 2 of 2

5 II B. Tech II Semester Supplementry Exmintions Jn/Fe FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science nd Engineering) Time: 3 hours Mx. Mrks: 75 Answer ny FIVE Questions All Questions crry Equl Mrks ~~~~~~~~~~~~~~~~~~~~~~~~~. ) Define NFA with 0-trnsition. Is the NFA s with 0-trnsitions re more powerful tht the NFA s without 0 -trnsition? Explin. ) Drw the trnsition digrm for elow FA. M= { {A,B,C,D}, {0,}, δ,c, {A,C} } δ (A,0) = δ (A,) = {A,B,C} δ(b,0) = B, δ(b,) = { A, C } δ(c,0) = {B,C}, δ(c,) ={ B, D } δ (D,0) = { A, B, C, D } δ(d,) = {A}. 2. ) Reduce the Moore mchine: A/x 0 B/y 0 C/y D/x 0 R0 SET ) Stte nd explin Myhill-Nerode theorem. (9M+6M) 3. ) Find Regulr expression corresponding to ech of the following susets over {0,}*. i) The set of ll strings contining no three consecutive 0 s. ii) The set of ll strings where the 0 th symol from right end is. iii) The set of ll strings over {0,} hving even numer of 0 s nd odd numer of s. iv) The set of ll strings over {0,} in which the numer of occurrences is divisile y 3 ) Descrie in detil out lgeric lws for regulr expressions. (8M+7M) 4. ) Give n equivlent left liner grmmr for the following right liner grmmr A 0 A A A A A A 0 ) Construct the CFG for the lnguge contining t lest one occurrence of. of 2

6 R0 SET ) Convert the following CFG into Chomsky Norml Form: S S S ) Explin in detil out pumping lemm for Context Free lnguges. (8M+7M) 6. ) Let G e CFG with the following productions. S B c A c B A C A B C c Construct PDA M such tht the lnguge generted y M nd G re equivlent. ) Wht is the dditionl feture PDA hs when compred with NFA? Is PDA superior over NFA in the sense of lnguge cceptnce? Justify your nswer. (9M+6M) 7. ) Give Turing mchine for the following tht computes ones complement of inry numer. ) Stte nd explin Church s hypothesis in detil. 8. ) Wht is Hlting prolem of Turing mchine? Is it decidle or undecidle? Explin. ) Write out Universl lnguge? Descrie out structure of universl Turing mchine nd out opertion on Turing mchine. 2 of 2

7 R0 SET - 4 II B. Tech II Semester Supplementry Exmintions Jn/Fe FORMAL LANGUAGES AND AUTOMATA THEORY (Computer Science nd Engineering) Time: 3 hours Mx. Mrks: 75 Answer ny FIVE Questions All Questions crry Equl Mrks ~~~~~~~~~~~~~~~~~~~~~~~~~. ) Wht is reltion? Discuss in detil out the properties of reltions. ) Give DFA s ccepting the following lnguges over the lphets{0,}: The set of strings such tht the numer of 0 s is divisile y five nd the numer of s is divisile y ) Design Mely mchine tht uses its stte to rememer the lst symol Red nd emits output y whenever current input mtches to previous one, nd emits n otherwise. ) Descrie in detil out conversion of NFA with - trnsitions to NFA without - trnsitions. 3. ) Wht is regulr expression? Descrie in detil out opertions nd pplictions of regulr expressions. ) Give the English description nd NFA for the following regulr expressions. i) r=(+0+00)*(+0+00) ii) r=[00++(0+0)(00+)*(0+0)]* 4. ) Construct the CFG for the lnguge L= n 2n where n ) Define grmmr. Explin in detil out different types of grmmrs. 5. ) Eliminte the -productions from the CFG s given elow: i) A 0B B B 0B B ii) S S S ) Remove the useless symols from the following grmmr: S A B cc A B B A C ccd D ddd (8M+7M) of 2

8 R0 SET ) Design push down utomt tht checks the well-formedness of prenthesis. ) Explin the procedure for construction of PDA from CFG. 7. ) Design the Turing mchine to compute following function f(x,y)=xy where x nd y re positive integers represented in unry. ) Explin the steps involved in construction of Turing mchine in detil. (8M+7M) 8. ) Find whether the post correspondence prolem P={(0,0),(0,),(0,0)} hs mtch. Give the solution. ) Show tht if L nd L re recursively enumerle, nd then L is recursive. (8M+7M) 2 of 2