Internet programming

• Circular Queue Full and Empty Boundary Conditions:
• Consider a circular queue of capacity $n - 1$ implemented using an array of size $n$, with index pointers FRONT and REAR:
• One empty slot is reserved to distinguish between full and empty states.
• Empty Condition: When no elements reside in the queue:

• Full Condition: When inserting one more element would advance REAR to meet FRONT:

• Conclusion: Full: (REAR+1) mod n == FRONT, empty: REAR == FRONT (Option 1).

Correct option: (1) Full: (REAR+1) mod n == FRONT, empty: REAR == FRONT

• Asymptotic Complexity Notations:
• Big-Omega ($\Omega$) Notation: Defines an asymptotic lower bound on the growth rate of an algorithm's execution time. Formally:

• Other Notations:
• Big-O ($O$): Asymptotic upper bound ($f(n) \le c \cdot g(n)$).
• Theta ($\Theta$): Asymptotically tight bound.
• Little-o ($o$): Strict upper bound.
• Conclusion: Omega (Option 1).

Correct option: (1) Omega

• Automata Theory in Compiler Construction:
• In modern programming languages (such as Java, C++, Python), tokens (identifiers, keywords, integer/float literals, operators) are specified via regular expressions.
• The necessary and sufficient theoretical machine model to recognize and tokenize regular languages is the Finite State Automata (FSA) (Deterministic or Non-Deterministic Finite Automata).
• Context-free syntax parsing requires Pushdown Automata, but lexical analysis requires only an FSA.
• Conclusion: Finite State Automata (Option 4).

Correct option: (4) Finite State Automata