Final answer:
A CFG for the expression a*bⁿnamⁿbmⁿcⁿ with n>0 and m≥0 is generated with the start variable S producing a followed by bⁿn and cⁿ using X, and Y producing amⁿbmⁿ with an epsilon for the case when m=0.
Step-by-step explanation:
To generate a Context-Free Grammar (CFG) for the given expression a*bⁿnamⁿbcⁿ where n>0, m≥0, we need to create a set of production rules that can produce strings that match the given pattern.
CFG Production Rules
- S → aXbc
- X → bXc | Y
- Y → aYb | ε
Step-by-step explanation:
- The start variable S produces a string starting with 'a' followed by the substring generated by X and ends with 'bc', which is the part where n>0 is satisfied.
- X recursively generates the substrings bⁿn and cⁿ where n>0. As it is specified that n is greater than zero, X cannot immediately go to Y; it must produce at least one 'b' and one 'c'.
- Y generates the strings corresponding to the part amⁿ which is then followed by bⁿ. Here, since m can be zero, we include the empty string ε as one of its productions, meaning it can produce nothing, thereby not adding additional 'a's or 'b's.