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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
build a TM that enumerate even set of even length string over a
phases of operational reaserch
Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or ev
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
design a turing machine that accepts the language which consists of even number of zero''s and even number of one''s?
Our DFAs are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state and input symbol. Thus, the ne
As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta
DEGENERATE OF THE INITIAL SOLUTION
designing DFA
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