If an initial ill of the pda A in Example 7.2 is (qo. aaeaa. 2 0). what
is the ill after the processing of aacaa? If the input string is (i) abeba.
(ii) abeb. (iii) acba. (iv) abac. (v) abab. will A process the entire
string? If so. what \vill be the final ill?
7.2 What is the ill that the pda A given in Example 7.5 reaches after
processing (i) a3b:. (ii) a:b3. (iii) as. (iv) b5. (v) b3
a:. (vi) ababab if
A starts with the initial ill?

 

 

ch7

 

 

 

7.3 Construct a pda accepting by empty store each of the following
languages.
(a) {a"blllalli m. 11 :2: I}
(b) {allb:" I 11 :2: I}
(c) {allblJle" I Tn. 11 2: I}
(d) {a'llbll 1m > 11 :2: I}
7.4 Construct a pda accepting by final state each of the languages given in
Exercise 7.3.

 

 

 

 

 

 

 

7.5 Construct a context-free grammar generating each of the following
languages. and hence a pda accepting each of them by empty store.
(a) {a" bll In :2: I} u {a'llb:m 1m :2: I}
(b) {d 'b'''all 1m. n :2: l} u {aile" In :2: I}
(c) {a"Yllellld" 1m. n :2: l}
7.6 Let L = {d"b!! In < m}. Construct (i) a context-free grammar accepting
L (ii) a pda accepting L by empty store. and (iii) a pda accepting L
by final state.
266 g Theory ofComputer Science

 

 

 

 

 

 

 

 

7.7 Do Exercise 7.6 by taking L to be the set of all strings over {a, h}
consisting of twice as many a's as b's.
7.8 Construct a pda accepting the set of all even-length palindromes over
{a, b} by empty store.
7.9 Show that the set of all strings over {a, b} consisting of equal number
of a's and b's is accepted by a detemunistic pda.
7.10 Apply the construction given in Theorem 7.4 to the pda M given in
Example 7.1 to get a context-free grammar G accepting N(M).

 

 

 

 

 

 

 

7.11 Apply the construction given in Theorem 7.4 to the pda obtained by
solving Exercise 7.4.
7.12 Show that {a"bl1 lll e: I} u {amb~'" 1m e: I} cannot be accepted by a
deterrninistic pda.
7.13 Show that a regular set accepted by a detemunistic finite automaton
with 11 states is accepted to final state by a deterministic pda with n
states and one pushdown symbol. Deduce that every regular set is a
deterministic context-free language.
(A context-free language is deterministic if it is accepted by a deterministic pda.)

 

 

 

 

 

 

 

7.14 Show that every regular set accepted by a finite automaton with 11 states
is accepted by a deterministic pda with one state and 11 pushdown
symbols.
7.15 If L is accepted by a detefllljnistic pda A. then show that L is accepted
by deterministic pda A which never adds more than one symbol at a
. (' 'f 5:( -) - ( I .) h I I < ) tlme l.e. 1 u q, a. ~. -q, y. t en YI _ -).

 

 

 

 

 

 

7.16 If L is accepted by a deterministic pda A, then show that L is accepted
by a deterministic pda A which always (i) removes the topmost symboL
or (ii) does not change the topmost symboL or (iii) pushes a single
symbol above the topmost symboL
 

 

 

4 Comparative Architectures
Outline the architecture of a simple dynamic department prediction cache that could provide high accuracy for branches with a good sized bias in one direction or the opposite (as an instance, loop-final branches). [5 points]
Give an instance of a easy code collection with branching that your structure would fail to foresee, and give an explanation for how it'd behave. [5 points]
It is feasible to create prediction caches that may reliably forecast branches whose behavior follows a quick regular sample by way of preserving a file of a branch's current conduct.
Revise your prediction cache layout to make use of a four-bit "local history" for
each entry. [5 marks]
How would this predictor perform with a branch displaying the following repeating
sequences?
(T = taken, N = no longer-taken)
(a) NTTNNTTNNTTN...
(b) NTTNNTNTTNNT...
(c) TNTTTTTNTTTT...
[5 marks]
5 Business Studies
What are the variations between earnings and loss and coins drift statements?
[5 marks]
What are the differences among debt and fairness finance? [5 marks]
What is an choice and how may it's valued? [5 marks]
Comment on the contemporary costs of excessive-tech shares. [5 marks]

CS
6. Retrieval of facts.
The most simple index keys for retrieval structures are easy natural language phrases.
Because the themes for which users are looking for to retrieve documents are often complex, it is from time to time asserted that attempting to find suits on any subset of a collection of submitted single-phrase keys is insufficiently discriminating.
Explain 3 awesome techniques to define word relationships in order that compound index phrases can be shaped. In assessment to (a) single terms and (b) the opposite  kinds of compound, you have to talk in detail how every is applied and what its execs and limitations are.
[6 marks for each method]
Which would you put into effect in a trendy-cause machine, and why?