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Automata and Compiler
(1) [25 marks] Let N be the last two digits of your student number. Design a finite automaton that accepts the language of strings that end with the last four bits of the binary expansion of N. (1.1) Make a regular expression ? of this language. For example the set of strings that end with 101 is expressed by a regular expression (0+1)*101. (1.2) Make an NFA that accepts this expression ?. You should remove any ?-moves that can be done trivially by inspection. (1.3) Make a subset automaton that accepts the language. (1.4) Perform state minimization on the above automaton.
(2) [25 marks] A CFG is given by S ? aSbS, S ? bSaS, S ? c
(2.1) Draw a syntax chart for this grammar. [5]
(2.2) Write a Python program for the recursive descent parser Trace the parser using two strings of at least 10 symbols, one for an accepted case and one for an unaccepted case. Do the trace using the style in the notes. [20]
(3) [25 marks] A sample program for computing the greatest common divisor by recursive call and its object program are given below. Some sample comments are given.
const a=75, b=55;
var x, y;
procedure gcd;
var w;
begin
if y>0 then begin
w:=y;
y:=x ? (x/y)*y;
x:=w;
call gcd;
end;
x:=a; y:=b;
write(x);
end.
0 jmp 0 21 Jump to 21, start of main
1 jmp 0 2
2 inc 0 4
3 lod 1 4
4 lit 0 0 Load literal 0
5 opr 0 12 Test if y>0
6 jpc 0 20 Jump to 20 if false
7 lod 1 4 Load y
8 sto 0 3 Store in w
9 lod 1 3
10 lod 1 3
11 lod 1 4
12 opr 0 5
13 lod 1 4
14 opr 0 4
15 opr 0 3
16 sto 1 4
17 lod 0 3
18 sto 1 3
19 cal 1 2
20 opr 0 0
21 inc 0 5
22 lit 0 75
23 sto 0 3
24 lit 0 55
25 sto 0 4
26 cal 0 2
27 lod 0 3
28 wrt 0 0 Write stack top
29 opr 0 0
proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .
phases of operational reaserch
#can you solve a problem of palindrome using turing machine with explanation and diagrams?
wht is pumping lema
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn
Ask question #Minimum 20 words accepted#
what is theory of computtion
Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)
dfa for (00)*(11)*
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