Comprehension

A machine is represented by states Q, input alphabet Σ, transition function δ. Initial state qo and final state F. The machine accepts all the strings over Σ = {a,b}, which starts and ended with any combination of all alphabet and abb works/lies in all the strings to be accepted 

For the above specified passage, which of the following represent the grammar for the language accepted the machine?

  1. S → AabbB, A → aA|∈, B → bB|∈
  2. S → abbA, A → aA|∈|bA
  3. S → AabbA, A → aA|bA|∈
  4. S → Aabb, A → aA|bA|∈

Answer (Detailed Solution Below)

Option 3 : S → AabbA, A → aA|bA|∈

Detailed Solution

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The correct answer is Option 3.

key-point-image Key Points
  • Option 3 specifies the grammar for the language accepted by the machine as follows:
    • S → AabbA
    • A → aA | bA | ε
  • This grammar generates strings where:
    • The start symbol S derives a string with 'A', followed by 'aabb', followed by 'A'.
    • The non-terminal A can be replaced by 'aA', 'bA', or ε (the empty string).
  • This allows for the generation of strings with 'a' and 'b' characters appropriately placed in the structure defined by the grammar.
additional-information-image Additional Information
  • Grammar rules (productions) define how strings in a language can be generated from the start symbol.
  • The symbol 'ε' denotes the empty string, which means a non-terminal can be replaced by nothing.
  • The use of non-terminals like A allows for recursive definitions, enabling the generation of complex strings.
  • Correct grammar formulations are essential in parsing and generating strings in programming languages and compilers.
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