CO2011: Automata Theory Assignment - Regular Expressions and Grammars

This document presents a solved assignment on automata theory, addressing key concepts such as register files, regular languages, and context-free grammars. The assignment explores the properties of regular expressions, including closure under various operations and their relationship to fi...Read More

AUTOMATA

Table of Contents
Question 1...................................................................................................................................................3
Question 2...................................................................................................................................................4
Question 3...................................................................................................................................................4
Question 4...................................................................................................................................................5
Question 5...................................................................................................................................................5
Question 6...................................................................................................................................................5
Question 7...................................................................................................................................................6
Question8....................................................................................................................................................6
Question 9...................................................................................................................................................6
References...................................................................................................................................................7

Question 1
A register file is a collection of K register is available on the memory storage that can be read
and written by specifying a register number that determines which register to be accessed and
identified on the memory. The reset the vector of the physical address is FFFF0h (16bytes on
1MB). The values of the register can be stored in the memory location of the ip register values is
0000. The reset processors are at an effective address of 0X0000100.
We can consider the 4 bit register of values is 0000, 1011, 1001, and 1010
Ex 1011two
1600000000000010110
0011 1011
1001 1010
Reset registers $0000
Store registers $0001
Add register $0001
1
--------
0010
The code of the register Σ={(Store,i),(Add,i),(Show,i),(reset)|i∈{0,1}4 is used for languages that
can specified the letters are separated by 0000
G={K},{a,b},{S->aKb,S->ab}.K).
The code of K is 0000, the code of a is 00001001, the code of b is 10000010 of the register ε ¿
| {z }
0000 1001001
| {z }
000 10101
| {z }
000 10011001
| {z }

00000 1010
The regular language of the final automata can be used for the each state transition of label with
which can move from one state to another.
Question 2
Let us consider L is not regular.
Where ε^e= Σ ∪ {ϵ}
Assume the alphabet languages are L⊆Σ is the regular language(S) is the power ser of S (all∗
possible subset of S). The input character for δ(·).The regular language of the NFA can be
calculating the values of set of states.
To show the closure under the competition, let., L ={s|s∈Σ −L}, Suppose that L is a regular∗
language. We can construct an NFA with a single final state for it.
In this L ={s|s∈Σ −L} transition of the NFA group we can making the initial vertex and set the∗
final vertex in reverse the direction on all edges.
Question 3
Let L1 and L2 be the regular expression language such that L(αγ)=L1,L(β)=L2.
L1+L2=L(αγ)+L(β) =L(αγ+β)
L1L2= L(αγ)L(β)=L(αγβ)
The computation of the α and β vlaues is
{L1L2:L1∈L1,L2∈L2}
{αγβ:αγ∈L1,β∈L2} the given solution is the odd values of the regular expression.
Assume the value of L1 is the {an :n is even}
Assume the value of L2 is {bm :m is odd}
If a is even, that can cover the "n"(an is even)
If a is odd then that can cover "a"(the even and odd property of "an" is determine by "X")
Given L1 is odd value
Given L2 is even value
I. L1 = L2 = {α∈{a,b} :|α|a =|α|b}∗
a. The regular language of the L values is even

II. L1 and L2 are regular,
a. For DFA for Σ having the L1 state such that is will accept the language L2 that∗
is defined as: all strings in L2 it’s accept the regular language. The NFA states
that accepts a language L1 and L2 (Flor, 2012).
Question 4
Question 5
Question 6
If L1 and L2 is the regular language of context free.
We know the L=L(s) for a DFA A, the terminal tokens are 0,1 and the production is
L→ 1L1 | 0L2 L2→ 0L2 | 1C C → | 0L2 | 1L1

Let Lx be the language generated by the grammar with S as the start symbol we prove that
L1∪L2 =c is the regular language.
L1 and L2 is the true expression of the context free languages
Question 7
The grammar of arithmetic expression is,
E −→ E+E | E−E | E E | E/E | (E) | 1∗
We can consider the set of terminal and non terminal symbols is {+,−, ,/,(,),1}.∗
The solved the arithmetic expression problem can be used for unambiguous grammar is
E-> E+T|E-T|E*T|E/T|id
E-> E+T|T T->T*T |id
E is the proper precedence between the two operations. But choice is in no way mandated by the
grammar. We must as well choose
E->E*T|T, T->T+T|id
it will generate the same strings, but using the different precedence to operators.
T->T+T| E/T|id
By using the non terminal and non terminal of the grammar rules that can use semantic
restriction of the expression is grammatically, to understand and make the grammar larger and
harder, parser of a compiler separate semantic check (Davidse et al., 2012).
Question8
The underlying data in naturally models as graph open sets of a scheme, which is used for
the regular expression language of the language. The finite automata of regular language module
that can use by store the memory register, the label variables, and edges labeled with regular
expression.
Question 9
The regular expression of the non terminal set of expression values is 42.

References
Davidse, K., Breban, T., Brems, L. and Mortelmans, T. (2012). Grammaticalization and
Language Change. Amsterdam/Philadelphia: John Benjamins Publishing Company.
Flor, N. (2012). Technology Corner: A Regular Expression Training App. Journal of Digital
Forensics, Security and Law.