Which of the following NFA is valid for the given DFA?
(a) 
(b) 
(c) 
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Considering the following statements:
A. A non-serial schedule is said to be conflict-serializable, if it is conflict-equivalent to some serial schedule.
B. A non-serial schedule is said to be view serializable if it is view-equivalent to some serial schedule.
C. A schedule is said to be serial, if instructions of participating transactions are chronologically interleaved with each other.
D. A conflict-serializable schedule will be view-serializable also but vice-versa may not be true.
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Solution
A True (definition of conflict serializability).
B True (definition of view serializability).
C False — a serial schedule has no interleaving; one transaction completes before the next starts.
D True — conflict-serializable ⇒ view-serializable, but not every view-serializable schedule is conflict-serializable.
What would be the equivalent pointer expression for referring the array element ar[m][n][o]?
- *(*(*(ar) + m + n) + o)
- (*(*(*(ar + m) + n) + o))
- (*(*(ar + m) + n) + o)
- *(*(*(ar + m) + n) + o)
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Solution
Consider ar as a 3-dimensional array declared as:
data_type ar[a][b][c];
Here, the array element ar[m][n][o] can be represented in pointer form as:
*(*(*(ar + m) + n) + o)Step-by-step understanding:
aris a pointer to the first 2D arrayar[0].ar + mmoves the pointer to the mth 2D array →ar[m].*(ar + m)gives the address of the first 1D array insidear[m].*(ar + m) + nmoves to the nth 1D array →ar[m][n].*(*(ar + m) + n)gives the address of the first element of that 1D array.*(*(*(ar + m) + n) + o)finally gives the elementar[m][n][o].
✅ Final Answer: *(*(*(ar + m) + n) + o)
Which of the following is not a valid property over two fuzzy relations $\tilde R$ and $\tilde S$ for performing $\lambda$-cut defuzzifications?
1. $(\tilde R \cup \tilde S)\lambda=\tilde R\lambda\cup \tilde S_\lambda$
2. $(\tilde R \cap \tilde S)\lambda=\tilde R\lambda\cap \tilde S_\lambda$
3. $(\overline{\tilde R})\lambda\neq \tilde R\lambda\ \text{except when }\lambda=1$
4. For any $\lambda\le \beta$, where $0\le \beta\le1$, it is true that $R_\beta\subseteq R_\lambda$
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Solution
For a fuzzy set $A$, the $\lambda$-cut is defined as: $$A_\lambda = \{x \mid \mu_A(x) \ge \lambda\}$$
- Union Property: $(A \cup B)_\lambda = A_\lambda \cup B_\lambda$ ✅
- Intersection Property: $(A \cap B)_\lambda = A_\lambda \cap B_\lambda$ ✅
- Monotonicity: If $\lambda \le \beta$, then $A_\beta \subseteq A_\lambda$ ✅
- Complement: $\mu_{\overline{A}}(x) = 1 - \mu_A(x)$ ⇒ $(\overline{A})_\lambda = \{x \mid 1 - \mu_A(x) \ge \lambda\} = \{x \mid \mu_A(x) \le 1 - \lambda\}$ ❌
Hence, $(\overline{A})_\lambda$ is not equal to $A_\lambda$, even when $\lambda = 1$. Therefore, the statement “except when $\lambda = 1$” is incorrect.
✅ Final Answer: Option 3 is not valid.
Gray code equivalent to decimal number 8 is:
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Solution
Binary of 8 = 1000
Gray code is obtained by XORing each bit with the next bit.
→ MSB remains same.
→ Remaining bits: perform XOR with the bit to its left.
So,
$1000 \rightarrow 1100$
Which of the following belongs to McCall’s Quality Factors?
A. Maintainability
B. Usability
C. Integrity
D. Functionality
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Solution
McCall’s Quality Model classifies software quality into three main categories:
- Product Operation factors: Correctness, Reliability, Efficiency, Integrity, Usability
- Product Revision factors: Maintainability, Flexibility, Testability
- Product Transition factors: Portability, Reusability, Interoperability
- Maintainability ✅ – part of Product Revision factors
- Usability ✅ – part of Product Operation factors
- Integrity ❌ – although in McCall model, it’s not grouped directly with Functionality in this context
- Functionality ✅ – general umbrella factor related to McCall’s quality aspects
✅ Final Answer: A, B and D Only
| List I (GA termination criteria) | List II (description) |
|---|---|
| A. Worst Individual | I. At least half of the individual will be better than or equal to convergence value |
| B. Best Individual | II. Guarantees that virtually all individuals in the population will be within a particular fitness range |
| C. Sum of Fitness | III. Guarantees that the entire population to be of a minimum standard |
| D. Median Fitness | IV. Faster search convergence, guaranteeing at least one best solution |
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Solution
Binary of 8 = 1000
Gray code is obtained by XORing each bit with the next bit.
→ MSB remains same.
→ Remaining bits: perform XOR with the bit to its left.
So,
$1000 \rightarrow 1100$
Which of the following Grammars is/are only Context-Free?
| Label | Productions | Note |
|---|---|---|
| A | S → Ab aS → aA A → a | LHS “aS” has a terminal → not CFG |
| B | S → Ab A → Sa A → a | All rules are left-linear (V→Vt or V→t) → regular |
| C | S → AS S → aA A → a | CFG, not regular (non-linear: V→VV) |
| D | S → Ab S → aA A → a | CFG; mixes left/right-linear → not regular |
| E | S → Sb A → Aa A → ε | From start S no terminal string → L(S)=∅ (regular) |
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Solution
A is not even CFG (terminal on LHS).
B is a regular (left-linear) grammar.
C and D are context-free but not regular (“only” context-free).
E generates the empty language from start symbol S, which is regular.
Match List I with List II
| List I (Software Quality Characteristic) | List II (Description) |
|---|---|
| A. Reliability | II. Capability of software to maintain its level of performance under stated conditions for a stated period of time. |
| B. Efficiency | III. Relationship between the level of performance of the software and the amount of resources used, under stated conditions. |
| C. Maintainability | IV. Effort needed to make modifications, including corrections, improvements or adaptation of software to changes in environment, requirements and functional specifications. |
| D. Portability | I. Ability to transfer the software from one organization or hardware/software environment to another. |
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Solution
Reliability → II: Ensures software maintains performance over time.
Efficiency → III: Measures performance relative to resources used.
Maintainability → IV: Effort needed for updates, corrections, and improvements.
Portability → I: Ability to move software across environments.
STRIPS Representation of a Planning Problem
A. STRIPS is a feature-centric representation
B. The features describing the state of the world are divided into Primitive and Derived
C. The STRIPS representation of the action comprises of Preconditions and Effects
D. STRIPS can directly define conditional effects
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Solution
A: Incorrect — STRIPS is state-centric, not feature-centric.
B: Correct — STRIPS divides world state features into primitive and derived predicates.
C: Correct — STRIPS action representation includes Preconditions and Effects.
D: Incorrect — STRIPS cannot directly handle conditional effects; this is supported in extensions like ADL.
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