ACtE05 · Chapter 5Networks & Security🏛️ Past Licensure QuestionID: 01fd6336

If $T_1$ and $T_2$ are two Turing machines executing in sequence where the output tape of $T_1$ serves as input to $T_2$ , this composite Turing machine is represented as:

Multiple Choice Options

A
T1 T2 (Concatenation / Sequential Composition)
✓ Correct Option
B
T1 ∪ T2 (Union)
C
T1 × T2 (Cartesian Product)
D
T1 + T2 (Direct Sum)

Detailed Technical Solution & Explanation

In Theory of Computation, the sequential composition (or concatenation) of two Turing machines $T_1$ and $T_2$ —where machine $T_1$ runs first to completion and halts in an accepting state, transferring head control and tape contents to $T_2$ —is denoted as $T_1 T_2$ .

Option Analysis:

•

Option A (T1 T2): Correct; standard mathematical notation for the sequential composition of Turing machines.

•

Option B (T1 ∪ T2): Represents the union (parallel/non-deterministic branching) of two languages.

•

Option C (T1 × T2): Represents multi-tape or Cartesian cross-product configurations.

•

Option D (T1 + T2): Arithmetic sum notation, not standard machine composition.

Reference: Mock Test 05NEC Licensure Syllabus

If $T_1$ and $T_2$ are two Turing machines executing in sequence where the output tape of $T_1$ serves as input to $T_2$ , this composite Turing machine is represented as:

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?

If $T_1$ and $T_2$ are two Turing machines executing in sequence where the output tape of $T_1$ serves as input to $T_2$ , this composite Turing machine is represented as:

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?