CS402 Theory of Automata. Theory of Automata. Lecture N0. 38 Reading Material. Introduction to Computer Theory Chapter 14

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1 C02 Theory of Automt Theory of Automt Lecture N0. 38 Reding Mteril Introduction to Computer Theory Chpter 1 ummry Exmple of PA with tle for running string, Equivlent PA, PA for EVEN EVEN Lnguge. Non- eterministic PA, Exmple of Non-eterministic PA, efinition of PUH OWN Automt, Exmple of Non-eterministic PA. TART PUH 1 2,, The process of running the string cn lso e expressed in the following tle TATE TART PUH PUH PUH 1 TACK Virtul University of Pkistn Pge 108

2 C02 Theory of Automt TATE TACK It my e oserved tht the ove PA ccepts the lnguge { n n : n=0,1,2,3, }. It my e noted tht the lphet Σ nd TACK lphet G, my e different in generl nd hence the PA equivlent to tht ccepting { n n : n=0,1,2,3 } discussed ove my e TART PUH X 1 X X 2 Following is n exmple of PA corresponding to n FA Exmple Consider the following FA corresponding to the EVEN-EVEN lnguge ± The corresponding PA will e Virtul University of Pkistn Pge 109

3 C02 Theory of Automt TART REA REA 3 Nondeterministic PA Like TGs nd NFAs, if in PA there re more thn one outgoing edges t REA or sttes with one lel, then it cretes nondeterminism nd the PA is clled nondeterministic PA. In nondeterministic PA no edge is leled y string of terminls or nonterminls, like tht cn e oserved in TGs. Also if there is no edge for ny letter to e red from the, the mchine crshes nd the string is rejected. In nondeterministic PA string my trce more thn one pths. If there exists t lest one pth trced y string leding to stte, then the string is supposed to e ccepted, otherwise rejected. Following is n exmple of nondeterministic PA TART 1 PUH PUH 2 3 Here the nondeterminism cn e oserved t stte. It cn e oserved tht the ove PA ccepts the lnguge EVENPALINROME= {w reverse (w): wœ{, } * } ={L,,,,,,, } Now the definition of PA including the possiility of nondeterminism my e given s follows PUHOWN AUTOMATON (PA) Pushdown Automton (PA), consists of the following Virtul University of Pkistn Pge 110

4 C02 Theory of Automt 1. An lphet of input letters. 2. An input with infinite mny loctions in one direction. Initilly the input string is plced in it strting from first cell; the remining prt of the is empty. 3. An lphet G of TACK chrcters.. A pushdown TACK which is initilly empty, with infinite mny loctions in one direction. Initilly the TACK contins lnks. 5. One TART stte with only one out-edge nd no in-edge. 6. Two hlt sttes i.e. nd sttes, with in-edges nd no out-edges. 7. A PUH stte tht introduces chrcters onto the top of the TACK. 8. A stte tht reds the top chrcter of the TACK (my contin more thn one out-edges with sme lel). 9. A REA stte tht reds the next unused letter from the (my contin more thn one out-edges with sme lel). Exmple: Consider the CFG Æ + * Following is the PA ccepting the corresponding CFL + * REA 3 TART + * PUH 1 REA PUH 2 PUH 5 PUH 3 + PUH 6 * PUH PUH 7 The string + * trces the pth shown in the following tle TATE TART PUH 1 PUH 2 PUH 3 + PUH TACK Virtul University of Pkistn Pge 111

5 C02 Theory of Automt TATE PUH 5 PUH 6 * PUH 7 REA 3 REA TACK * * * * * * It my e noted tht the letters re deleted from the insted of underlined. It my lso e noted tht the choice of pth t stte cn e determined y the left most devition of the string elonging to the CFL. Virtul University of Pkistn Pge 112