Question

Convert the grammar below to Chromsky Normal Form:

U --> Vab| S

T--> abS|E

Answer #1

Convert the grammar G = ({S,A,B,C},{a,b},P,S), where P is
given below, into the Chomsky Normal Form.
S −→ AaA | AB
A −→ BB | bAA | ε
B −→ bS | b | ε

Convert the following CFL grammar to an equivalent grammar in
Chomsky normal form. A → BAB | B | ε B → OO | ε

1. Put the following grammar into Chomsky Normal Form. Note that
this grammar has no useless symbols.
S → iSE | a E → eS | ε

Obtain a grammar in Chomsky Normal Form (CNF) equivalent to the
grammar G with productions P given
S ->aAb | B
A ->aA | a
B-> bB | b

Consider the following context-free grammar: S → TT | U T → 0T |
T0 | # U → 0U00 | # a. Give a parse tree for the string: 0#0#0 b.
Give a leftmost derivation for the string: 00#0000

1. Find the Laplace transform of
a.) f(t)=u(t−4)⋅e^t
F(s)=
2. Find the inverse Laplace transform of
a.) F(s)=2e^(−3s)−e^(−2s)−3e^(−6s)−e^(−9s)/s
f(t) =
b.) F(s)=e^(−6s)/s^2−3s−10
f(t) =
c.) F(s)=4e^(−9s)/s^2+16
f(t) =

Prove or give a counter-example:
(a) if R ⊂ S and T ⊂ U then T\ S ⊂ U \R.
(b) if R∪S⊂T∪U, R∩S= Ø and T⊂ R, then S ⊂ U.
(c) if R ∩ S⊂T ∩ S then R⊂T.
(d) R\ (S\T)=(R\S) \ T

Convert the following CFG to its equivalent CNF.
S → aa S ddd | T
T → b T cc | ε

Utility Function: U(t, s) = 4ts
Price of t: Pt = $5
Price of s: Ps = $10
Income: M = $100
(Assume that t is measured on the horizontal axis and s is
measured on the vertical axis.)
a. Write the equation of the Budget Line in the form of total
spending = income. Plug in specific numerical values.
b. Solve for the values of t and s that maximize the Utility
Function subject to the Budget Line to...

Convert (and simplify) the following sentences to Conjunctive
Normal Form (CNF):
2.1. (P →Q) → ((Q → R) → (P → R))
2.2. (P → Q) ↔ (P → R)

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