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Midterm 1 Breakdown

Midterm 1 Breakdown. >79 3 >29 7 >69 5 >19 5 >59 7 >49 9 >39 7. Project 1. CS 3240: Languages and Computation. Context-Free Languages. What are Grammars?. A grammar G is defined by (V, T , P, S), where V is a finite set of variables

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Midterm 1 Breakdown

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  1. Midterm 1 Breakdown >79 3 >29 7 >69 5 >19 5 >59 7 >49 9 >39 7

  2. Project 1

  3. CS 3240: Languages and Computation Context-Free Languages

  4. What are Grammars? • A grammar G is defined by (V, T, P, S), where • V is a finite set of variables • Tis a finite set of terminal symbols • P is a finite set of productions or ules • SV is the special start variable • Each grammar G defines a language L(G), which is the set of strings in T* (=Σ*) that G can generate from S. • Automata are actuated by the transition table, grammars by the production rules.

  5. Context-Free Grammars • A context-free grammar (V, T, P, S) is a grammar where all production rules are of the form: A → x, with AV and x(VT)*A string in (VT)* is called sentential form • E.g., let G = ({S}, {a,b}, P , S) with for P: • S→aSa • S→bSb • S→. • Some derivations from this grammar: • S  aSa  aaSaa  aabSbaa  aabbaa • S  bSb  baSab  baab, and so on. • In general S …. wwR for w{a,b}*.

  6. Beyond regular Languages

  7. Formal definition of CF Grammar & Language

  8. Another CFG Example Consider the CFG G=({S,Z},{0,1}, P, S) with P: S  0S1 | 0Z1 Z 0Z |  What is the language generated by this G? Answer: L(G) = {0i1j | ij } Specifically, S yields the 0j+k1j according to:S  0S1  …  0jS1j  0jZ1j  0j0Z1j …  0j+kZ1j  0j+kε1j = 0j+k1j

  9. Exercise • Design CFGs for the following languages: • { 0n1n : n≥0} • { 0n1m : n,m≥0} • { (0|1)* : # of 0s > # of 1s} • Answers: • S → 0S1 |  • S → 0S | R and R → 1R |  • S → T0T and T → TT | 0T1 | 1T0 | 0 | 

  10. derivations

  11. Leftmost righmost

  12. Sentential forms

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