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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
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)
Ask question #Minimum 20 words accepted#
automata of atm machine
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, dif
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turing machine
what are the advantages and disadvantages of wearable computers?
We developed the idea of FSA by generalizing LTk transition graphs. Not surprisingly, then, every LTk transition graph is also the transition graph of a FSA (in fact a DFA)-the one
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