GATE CSE 2008
Q42.
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that the studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that the studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?Q43.
The P and V operations on counting semaphores, where s is a counting semaphore, are defined as follows: P(s) : s = s - 1; if (s < 0) then wait; V(s) : s = s + 1; if (s <= 0) then wakeup a process waiting on s; Assume that P_{b} and V_{b} the wait and signal operations on binary semaphores are provided. Two binary semaphores x_{b} and y_{b} are used to implement the semaphore operations P(s) and V(s) as follows: P(s) : Pb(xb); s = s - 1; if (s < 0) { Vb(xb) ; Pb(Yb) ; } else Vb(xb); V(s) : Pb(xb) ; s = s + 1; if (s <= 0) Vb(Yb) ; Vb(xb) ; The initial values of xb and yb are respectivelyQ44.
Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following: Each finite state automaton has an equivalent pushdown automatonQ45.
P and Q are two propositions. Which of the following logical expressions are equivalent? I. P\vee \sim Q II.\sim (\sim P \wedge Q) III.(P \wedge Q)\vee (P\wedge \sim Q)\vee (\sim P\wedge \sim Q) IV. (P\wedge Q)\vee \vee (P\wedge \sim Q)\vee (\sim P\wedge Q)Q46.
Let x_{n} denote the number of binary strings of length n that contain no consecutive 0s. The value of x_{5} isQ47.
Let x_{n} denote the number of binary strings of length n that contain no consecutive 0s. Which of the following recurrences does x_{n} satisfy?Q48.
Which of the following are regular sets? I. \{a^{n}b^{2m}|n\geq 0,m\geq 0\} II. \{a^{n}b^{m}|n=2m\} III. \{a^{n}b^{m}|n\neq m\} IV. \{xcy|x,y,\in \{a,b\}^*\}Q50.
Let R and S be two relations with the following schema R (\underline{P},\underline{Q},R1,R2,R3) S (\underline{P},\underline{Q},S1,S2) Where {P, Q} is the key for both schemas. Which of the following queries are equivalent? I. \Pi _{P}(R\Join S) II. \Pi _{p}(R)\Join \Pi _{P}(S) III. \Pi _{P}(\Pi _{P,Q}(R)\cap \Pi _{P,Q}(S)) IV. \Pi _{P}(\Pi _{P,Q}(R)-(\Pi _{P,Q}(R)-\Pi _{P,Q}(S)))