Consider the 5-state DFA M accepting the language 𝐿(𝑀) ⊂ (0 + 1)^* shown below. For any string 𝑤 ∈ (0 + 1)^* let 𝑛₀(𝑤) be the number of 0 ′ 𝑠 in 𝑤 and 𝑛₁(𝑤) be the number of 1′𝑠 in 𝑤.

Which of the following statements is/are FALSE?

Consider the following read-write schedule S over three transactions T1,T2,T3 where the subscripts in the schedule indicate transaction IDs

S: r₁(z), w1(z), r2(x), r3(y), w3(y), r2(y), w2(x), w2(y)

Which of the following transaction schedules is/are conflict equivalent to S?

Let G be the directed graph and T a DFS spanning tree in G such that it is rooted at vertex v. Suppose T is also Breadth First Search (BFS) Tree in such as rooted at v .Which of the following options is/are TRUE for every such graph G and tree T?

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

Consider a binary min-heap containing 105 distinct elements. Let k be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of k is

Consider the following recurrence relation:

T(n)={√n T(√n)+n} for n>=1 
T(n)=1 for n=1

Which one of the following options is CORRECT ?

An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified array?

Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a = b = 1. Though context switching between threads can happen at any time, each statement of T1 or T2 is executed atomically without interruption.

T1 T2
a = a + 1; b = 2 * b;
b = b + 1; a = 2 + a;

Which one of the following options lists all the possible combinations of values of a and b after both T1 and T2 finish execution? 

Consider the following pseudo-code

L1: t1 = -1
L2: t2 = 0
L3: t3 = 0
L4: t4 = 4 * t3
L5: t5 = 4 * t2
L6: t6 = t5 * M
L7: t7 = t4 + t6
L8: t8 = a[t7]
L9: if t8 <= max goto L11
L10: t1 = t8
L11: t3 = t3 + 1
L12: if t3 < M goto L4
L13: t2 = t2 + 1
L14: if t2 < N goto L3
L15: max = t1

Which one of the following options CORRECTLY specifies the number of basic blocks and the number of instructions in the largest basic block, respectively?

Consider the following grammar G, with 𝑆 as the start symbol. The grammar G has three incomplete productions denoted by (1), (2), and (3).

 𝑆 → 𝑑𝑎𝑇 | (1) 
𝑇 → 𝑎𝑆 | 𝑏𝑇 | (2) 
𝑅 → (3) | 𝜖 

The set of terminals is {𝑎, 𝑏, 𝑐, 𝑑, 𝑓}. The FIRST and FOLLOW sets of the different non-terminals are as follows.

FIRST(𝑆) = {𝑐, 𝑑, 𝑓}, FIRST(𝑇) = {𝑎, 𝑏, 𝜖}, FIRST(𝑅) = {𝑐, 𝜖}
FOLLOW(𝑆) = FOLLOW(𝑇) = {𝑐, 𝑓, $}, FOLLOW(𝑅) = {𝑓} 

Which one of the following options CORRECTLY fills in the incomplete productions?