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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
For every regular language there is a constant n depending only on L such that, for all strings x ∈ L if |x| ≥ n then there are strings u, v and w such that 1. x = uvw, 2. |u
shell script to print table in given range
Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}
Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi
Myhill graphs also generalize to the SLk case. The k-factors, however, cannot simply denote edges. Rather the string σ 1 σ 2 ....... σ k-1 σ k asserts, in essence, that if we hav
dfa for (00)*(11)*
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
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