1*(011*)*00(11*0)* 1* intersect 0*(100*)*11(00*1)* 0*
The first half of the regular expression should match all binary strings with one pair of consecutive 0s and the second half should match all binary strings with one pair of consecutive 1s. As the first contains strings with one pair of consecutive 1s, and the second contains strings with one pair of consecutive 0s, I claim that the entire regular expression would only match binary strings with at most one consecutive pair of 0s and one consecutive pair of 1s. Is this correct?
Yes, but more precisely your expression matches binary strings that contain exactly one pair of 0s and exactly one pair of 1s (rather than "at most").
I can prove it via this method:
Here is another regular expression to encode those semantics, using a union rather than an intersection, which I feel is more straightforward.
(1)?(01)*00(10)*11(01)*(0)?|(0)?(10)*11(01)*00(10)*(1)?
The first half matches binary strings in which the pair of zeros precedes the pair of ones, and the second half matches binary strings in which the pair of ones precedes the pair of zeros. Before, after, and between those pairs alternating values may occur.
A string is accepted if it matches either of those patterns (rather than both as in your expression).
Now, it is possible to construct the state transitions based on either of these regular expressions. I have done so below, first with mine then with yours. Each numbered state contains a list of regular expressions that describe the remaining portion of the string, and the state transitions that occur when either a 0, 1, or end-of-line is encountered. A string matches if it matches any regular expression in the list.
As you can see, the state transitions between your version and mine are completely homologous. Therefore, they represent exactly the same set of strings.
start (1)?(01)*00(10)*11(01)*(0)?
(0)?(10)*11(01)*00(10)*(1)?
0 1
1 2
EOL NO_MATCH
1 1(01)*00(10)*11(01)*(0)?
0(10)*11(01)*(0)?
(10)*11(01)*00(10)*(1)?
0 3
1 2
EOL NO_MATCH
2 (01)*00(10)*11(01)*(0)?
0(10)*11(01)*00(10)*(1)?
1(01)*00(10)*(1)?
0 1
1 4
EOL NO_MATCH
3 (10)*11(01)*(0)?
0 NO_MATCH
1 5
EOL NO_MATCH
4 (01)*00(10)*(1)?
0 6
1 NO_MATCH
EOL NO_MATCH
5 0(10)*11(01)*(0)?
1(01)*(0)?
0 3
1 7
EOL NO_MATCH
6 1(01)*00(10)*(1)?
0(10)*(1)?
0 8
1 4
EOL NO_MATCH
7 (01)*(0)?
0 9
1 NO_MATCH
EOL MATCH
8 (10)*(1)?
0 NO_MATCH
1 10
EOL MATCH
9 1(01)*(0)?
END
0 NO_MATCH
1 7
EOL MATCH
10 0(10)*(1)?
END
0 8
1 NO_MATCH
EOL MATCH
start 1*(011*)*00(11*0)*1* + 0*(100*)*11(00*1)*0*
0 1
1 2
EOL NO_MATCH
1 11*(011*)*00(11*0)*1* + 0*(100*)*11(00*1)*0*
0(11*0)*1* + 0*(100*)*11(00*1)*0*
0 3
1 2
EOL NO_MATCH
2 1*(011*)*00(11*0)*1* + 00*(100*)*11(00*1)*0*
1*(011*)*00(11*0)*1* + 1(00*1)*0*
0 1
1 4
EOL NO_MATCH
3 (11*0)*1* + 0*(100*)*11(00*1)*0*
0 NO_MATCH
1 5
EOL NO_MATCH
4 1*(011*)*00(11*0)*1* + (00*1)*0*
0 6
1 NO_MATCH
EOL NO_MATCH
5 1*0(11*0)*1* + 00*(100*)*11(00*1)*0*
(11*0)*1* + 00*(100*)*11(00*1)*0*
1*0(11*0)*1* + 1(00*1)*0*
(11*0)*1* + 1(00*1)*0*
0 3
1 7
EOL NO_MATCH
6 11*(011*)*00(11*0)*1* + 0*1(00*1)*0*
0(11*0)*1* + 0*1(00*1)*0*
11*(011*)*00(11*0)*1* + 0*
0(11*0)*1* + 0*
0 8
1 4
EOL NO_MATCH
7 1*0(11*0)*1* + (00*1)*0*
1* + (00*1)*0*
0 9
1 NO_MATCH
EOL MATCH
8 (11*0)*1* + 0*1(00*1)*0*
(11*0)*1* + 0*
0 NO_MATCH
1 10
EOL MATCH
9 (11*0)*1* + 0*1(00*1)*0*
(11*0)*1* + 0*
0 NO_MATCH
1 7
EOL MATCH
10 1*0(11*0)*1* + (00*1)*0*
1* + (00*1)*0*
(11*0)*1* + 0*
0 8
1 NO_MATCH
EOL MATCH