Final answer:
A grammar for L = {a^n where n is even} in the context of formal languages can be represented as 'S → aS | ε', where 'S' is replaced with 'aS' to add two 'a's or with ε for closure.
Step-by-step explanation:
The student is asking for a grammar that generates the language L = {aⁿ where n is even}. In the context of formal languages and automata theory in computer science, a grammar is a set of production rules for strings in a formal language. The strings consist of terminal and non-terminal symbols. To define a grammar for this particular language, we will use a simple context-free grammar (CFG).
A suitable grammar for L = {aⁿ where n is even} is as follows:
Here 'S' is the start variable. This grammar says that 'S' can either be replaced with 'aS', which adds two 'a's to the string (thus maintaining the even count of 'a's) or it can be replaced with ε (the empty string), which is necessary to conclude the string production. The ε symbol represents the empty string, and its inclusion allows for the generation of the string with zero 'a's, which is an even number, satisfying the requirement for n to be even.