Prove that the language given by the CFG below is not regular. S + PPQ P...
10. Consider the following CFG: Is the language generated by this CFG a regular language? If so, give a regular expression denoting it. If not, prove it.
10. Consider the following CFG: Is the language generated by this CFG a regular language? If so, give a regular expression denoting it. If not, prove it.
Please help with the question below. Make sure that the answer
is legible, Thanks.
1. Prove that every finite language is regular. Hint: Give a constructive proof that explains how to start with a finite language (set of strings) A and then build an NFA that accepts any string in A. There is a "brute force" style of NFA that ends up with a total of el-1wl states. Sketch the NFA corresponding to 4 (00, 11, 101)
1. Consider machine M-(Q, Σ. Γ. δ.ql, qaccept, qreject), where Q-{qi, q2, q3, qaccept, qreject}, -{0.1), Г-{0.1 Ủ}, and the transition function as follows is δ (qi, U)-Greject, U, R) Prove that M is NOT a decider Describe in mathematical terms the language A that M recognises, and verify 1. ii. your answer, ie prove that A-L(M) iii. Is A Turing-decidable? [No need for a formal proof, but give clear reasons for your answer
1. Consider machine M-(Q, Σ. Γ....
Additional 9-14 Prove that the language {a"b" n, k ε N and n S k} is not regular Hint: I go over this proof in the lecture. You can watch it again to make sure you follow it before doing it. 2 Additional 9-15 Prove that the language (a"b n, k E N and n Hint: a little different... 2 k Is not regular 3 Additional 9-16 Prove that the language (w w (a, b and w has an equal...
3. Create a CFG describing regular expressions over the alphabet {0, 1}. You will need to quote the regular expression operators and the template given you has them quoted as terminals. We expect the grammar to generate the following syntactic constructions: • Union via "|", for example, 0 1 "|" 1 should be in the language generated by the grammar • Intersection via "&", for example, 0 1 "&" 1 should be in the language • Concatenation: any nonempty sequence...
1) Webber Chap. 11 Exercise 1 Prove that {a"b"c"} is not regular. Hint: Copy the proof of Theorem 11.1-only minor alterations are needed. Theorem 11.1 The language {a"b"} is not regular. • Let M = (Q, {a,b}, 8, 9., F) be any DFA over the alphabet {a,b}; we'll show that L(M) + {a"b"} • Given as for input, M visits a sequence of states: - *(q,,ɛ), then 8*(q,,a), then 8*(9,,aa), and so on • Since Q is finite, M eventually...
1. Use a truth table in canonical form below to show that ¬p∧q and ¬p∧¬q are not equivalent. Feel free to make necessary adjustments to the table. p q p∧q ¬p ¬q ¬p∧q ¬p∧¬q 2. Tell whether the following two expressions are equivalent by constructing their truth tables in canonical form. You may make necessary adjustments to the table provided below. Is p∨q∧rlogically equivalent to p∨q∧p∨r? p q r q∧r p∨q p∨r 3. Prove or Disprove (make sure to show...
2. Problem: Given Q(x)=2(2-1) . Give a step-by-step(δ Proof to prove that: lim QCx) 1. ing the ε-δ definition you are using for this problem in terms of the formula of Q(x) and limit value
Problem #5 [30 Points) Prove each of the following statements by Mathematical Induction. Make sure you check P(1), state P(n+1), and give a complete proof of P(n) = P(n+1), n > 1. A. n.(n+1)(n+2) n 1. P(n): 1. 2+2-3+3.4+...+n·(n + 1) = - to od to be used B. P(n): (1 + a)" > 1+na, a>0,,n>1. ) han de stem
proving that the language of the grammar is the given one. Prove by induction on n that sum of 2^k for k = 0 to n = 2^(n+1) -1 for n>=0 Basis P(0) when n = 0: ** = ** is true. Assume P(i) is true, AL = AR when n = i: ** = ** for i>=0 Inductive Step P(i) to P(i+1), Show when n = i+1: ** = ** ...