Final answer:
The CFG provided can generate the strings 001100 and 01100. These strings adhere to the production rules of the CFG which require the numbers of 0s and 1s to be mirrored around the center of the string.
Step-by-step explanation:
The Context-Free Grammar (CFG) given in the question can generate strings where the number of 0's match the number of 1's on each side of the string. This is because the production rules A => 0A0 and A => 1A1 ensure that for every 0 or 1 added on the left side, there is a corresponding 0 or 1 on the right side. An important aspect to consider is whether the CFG can generate strings with balanced mirrored halves around the center.
Let's analyze each string:
- 001100: This string can be generated by the CFG by using the production A => 0A0 two times followed by A => epsilon.
- 0011: This string cannot be generated by the CFG because the number of 0's and 1's are not mirrored around the center.
- 001110: This string also cannot be generated by the CFG as the numbers 0 and 1 are not balanced and mirrored.
- 01100: This string can be generated by the CFG by using the production A => 0A0 followed by A => 1A1, and lastly A => epsilon.
Therefore, the strings that can be generated by this CFG are 001100 and 01100.