Mathematical Foundation of Computer Science

DHARM 264 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE For accepting the reverse of the strings of Language L, we can construct t ...

DHARM REGULAR AND NONREGULAR LANGUAGES 265 To answer the question let M = (Q, Σ δ, q 0 , F) be a DFA accepts language L, i.e. L ...

DHARM 266 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE 10.5. 3(DP 3)-Membership Problem Another important decision problem is, fo ...

DHARM REGULAR AND NONREGULAR LANGUAGES 267 10.5.5 Minimization Problem and Myhill Nerode Theorem (Optimizing DFA)........ The Mi ...

DHARM 268 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE We say that equivalence relation RK exists between states r and s (pRKq). ...

DHARM REGULAR AND NONREGULAR LANGUAGES 269 And, PR 0 S ⇒δ(P, ∈) = P(∉ F) and δ(S, ∈) = S(∉ F) so they are Distinguishable. Simil ...

DHARM 270 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Since, we couldn’t find any equivalent of states in this group so there is ...

DHARM REGULAR AND NONREGULAR LANGUAGES 271 Example 10.7. Find a minimum states DFA of the finite automata shown in Fig. 10.14 wh ...

DHARM 272 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE EXERCISES 10.1 Prove or disprove the regularity of the following languages ...

DHARM REGULAR AND NONREGULAR LANGUAGES 273 (iii) A B D E F G C 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 (iv) d e a c b f 0 0 0 0 0 0 1 1 1 ...

DHARM 274 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE x.y = a 1 a 2 ............... an. b 1. b 2 ................ .. bn q 0 q 1 ...

NON-REGULAR GRAMMARS 11.1 Introduction.......................................................................................... ...

11.1INTRODUCTION We know that finite automata gives the abstract view of computation and the regular languages tell about the po ...

DHARM NON-REGULAR GRAMMARS 277 Each grammar must start with a symbol which is called start symbol; all other symbols (terminals/ ...

DHARM 278 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE l A production of type bABc → babbc is certainly a valid production. On le ...

DHARM NON-REGULAR GRAMMARS 279 Regular Language Co nt ext SensitiveLang ua ge C on tex tFreeLangu ag e Re cu rsi veE numerableLa ...

DHARM 280 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Hence we say that if, α 1 ⇒α 2 ⇒α 3 ⇒ .........αn–1 ⇒αn then,α 1 ⇒N αn or ...

DHARM NON-REGULAR GRAMMARS 281 Then L (G) contains following strings: S ⇒ aaaa; S ⇒ aaaaS ⇒ aaaa aaaa; S ⇒ aaaaS ⇒ aaaa aaaaS ⇒ ...

DHARM 282 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE l Starting state (q 0 ) will corresponds to the starting symbol S, and l S ...

DHARM NON-REGULAR GRAMMARS 283 Since S and A are the final states hence, following are some more productions: l Start state is t ...