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Module 4: Turing Machines (TM)

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If an infinite language is passed to Machine MM, the subsidiary which gives a finite solution to the infinite input tape is:

(i) Compiler
(ii) Interpreter
(iii) Loader and Linkers
(iv) None of the mentioned

Worked SolutionAI Assisted

Answer

Correct Option: (iv) None of the mentioned

Explanation

An infinite language requires a machine with unbounded memory. In the Turing Machine model M=(Q,Σ,Γ,δ,q0,B,F)M = (Q, \Sigma, \Gamma, \delta, q_0, B, F) the tape is infinite, but the finite control itself is finite.

  • Compiler: Translates a high-level program to target code before execution. It does not provide run-time handling of an infinite input tape; it assumes input is finite source text.
  • Interpreter: Executes source line-by-line, still requires entire input to be presented finitely; it does not make an infinite tape finite.
  • Loader and Linkers: Perform loading / relocation of object code into memory. They handle finite modules, not an infinite language / infinite tape.

The subsidiary that actually gives a finite description of an infinite computation is the finite control (finite automaton) + the Turing Machine’s transition function or, in language theory, the finite representation (regular expression / grammar / TM description) itself. None of the three listed system softwares fulfills this role.

The theoretical concept is:

  • Infinite language L⊆Σ∗L \subseteq \Sigma^* is described finitely by a grammar / regular expression / TM encoding ⟨M⟩\langle M \rangle, not by compiler/interpreter/loader.

Hence none of (i)-(iii) is correct.

Final Answer

None of the mentioned. The finite solution is provided by the finite control / finite encoding ⟨M⟩\langle M\rangle of the machine, not by compiler / interpreter / loader.

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