Question

**Question 1**

Consider the following grammar G:

S ➝ A B C | A C | A | B

A ➝ a B

B ➝ b C | a

C ➝ c D

D ➝ d A

Recall that a non-terminal A is reachable if there is a derivation starting from S in which A appears: S ⇒* x A y holds for some x and y which are sequences of terminals and non-terminals (possibly empty). For example, if there are only two rules S → a A and B → a , then A is reachable because S ⇒ a A is a derivation starting from S in which A appears. On the other hand B is not reachable because there is no derivation starting from S in which B appears. Which of the following are the reachable symbols of the grammar G above?

a) A, B, C, D, and S -- Correct Answer

b) S only

c) None of the above

d) A, B, and C only

e) A, B, and S only

**Question 2**

Consider the following grammar G:

S ➝ A B C | A C | A | B

A ➝ a B

B ➝ b C | a

C ➝ c D

D ➝ d A

Recall that a non-terminal A is useful if there is a derivation
of a string of terminals starting from S in which A appears: S ⇒* x
A y ⇒* w holds for some x and y which are sequences of terminals
and non-terminals (possibly empty) and some w which is a sequence
of terminals (possibly empty). For example, if there are only three
rules S → a A, A → B and B → a , then A is useful because S ⇒ a A ⇒
a B ⇒ a a is a derivation of the sequence of terminals a a starting
from S and in which A appears. If A is not useful, then we say that
it is useless. Which of the following are the
**useless** symbols of the grammar G above?

a) All non-terminals are useless

b) A, C, and D only

c) D only

d) None of the above -- Correct Answer

e) C and D only

Can someone explain the concept and how to come up with the answers to these questions?

Answer #1

Consider the following grammar. Nonterminals are lowercase and
terminals are uppercase.
s -> c A
c -> c B | B
Which of the following sentences is in the language generated by
the grammar?
a) BAA
b) BBBA
c) BBAAAAA
d) none of the above

Consider the grammar G with productions as follows:
S → AD | BC
A → a
B → b
C → a | AS | BE
D → b | BS | AF
E → CC
F → DD
Use the CYK algorithm to test membership of abbaba.

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

Automata Theory and Formal Languages
Problems 1: Consider the following two
grammars.
Grammar G1- S → aSb / ∈ Grammar G2- S → aAb / ∈, A → aAb / ∈
a. is G1=G2
b. What is the grammar generated by the expression
Problem 2: Let us consider the grammar.
G2 = ({S, A}, {a, b}, S, {S → aAb, aA → aaAb, A → ε } )
Derive aaabbb
Problem 3: Suppose we have the following
grammar.
G: N...

1. Consider the reaction A(g) + B(g) ↔ C(g) + D(g) at 300°C.
What is the equilibrium concentration of D if the initial
concentrations are [A] = [B] = 1.25 x 10-2 M and [C] =
[D] = 3.50 x 10-3 M? The value of the equilibrium
constant for the reaction is 55.9 at 300°C.
1.41 x 10-2 M
4.39 x 10-2 M
8.34 x 10-2 M
6.62 x 10-2 M
5.76 x 10-2 M
9.18 x 10-3 M
2....

Which of these species has the highest entropy (S°) at
25°C?”
A) HF(g) B) NaF(s) C) SiF4(g) D) SiH4(g) E) Al(s)

a) Starting with only NO(g), what will be the predominate
specie(s) present at equilibrium? N2(g) + O2(g) ↔ 2NO(g) Kc = 4.6 x
10-31. b) If [N2] = [O2] = 8.6 x 10-2M and [NO] = 5.0 x 10-20, is
the system in equilibrium? If not, what which way will it go to
reach equilibrium? c) If, at equilibrium, [N2] = [O2] = 8.6 x
10-2M, what is the equilibrium concentration of NO?
Answers: a). N2 and O2
b). no,...

Consider the following generic reaction for which K =
0.00551:
2 A + 3D ⇄ E
Which of the following correctly applies to this reaction:
Products are favored at equilibrium.
Rateforward = Ratereverse
Keq =
[E]
[A]2[D]3
Keq =
[A]2[D]3
[E]
View Available Hint(s)
Consider the following generic reaction for which K =
0.00551:
2 A + 3D ⇄ E
Which of the following correctly applies to this reaction:
Products are favored at equilibrium.
Rateforward = Ratereverse
Keq =
[E]...

Consider y = 1 + 3x– 4x3.
a. State the
domain. ____________
b. State the
range. ____________
c. Find the
y-intercept. ____________
d. Find the
x-intercept(s). ____________
e. State the equation of the horizontal
asymptote, if any. ____________
f. State the equation of the slant
asymptote, if
any. ____________
g. State the equation of the vertical
asymptote, if any. ____________
h. State the interval(s) on which the
function is
decreasing. ____________
i. State the interval(s) on which the
function is
increasing. ____________
j. Find
dy/dx. ____________
k. Find the local...

Refer to the reaction system C(s) + H2O(g) ↔ CO(g) + H2(g) at
equilibrium for which ΔH°rxn = +131 kJ. Assume ideal gas behavior.
Predict the direction in which the above equilibrium will shift as
a result of the stated change in conditions.
a) An increase in the reaction temperature.
b) A decrease in the amount of C(s).
c) A decrease in the reactor volume.
d) An increase in PH2O.
e) Addition of N2 gas to the reaction mixture.

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