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GATE 1988 Computer Science Questions

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GATE CSE 1988 | Question: 17i-ii-iii
The following table gives the cost of transporting one tonne of goods from the origins A, B, C to the destinations F, G, H. Also shown are the ... above, calculate the values of the duals and determine whether this is an optimal solution.
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GATE CSE 1988 | Question: 16ii-iii
If $x \| \underline{x} \| \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ ... easy to calculate for any matrix, explain why the condition number is difficult (i.e. expensive) to calculate.
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GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
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GATE CSE 1988 | Question: 15
Consider the DFA $M$ and NFA $M_{2}$ as defined below. Let the language accepted by machine $M$ be $L$. What language machine $M_{2}$ accepts, if$F2=A?$F2=B?$F2=C?$ ... F \}$D=\{\langle p, q, r \rangle \mid p,q \in Q; r \in F\}$
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GATE CSE 1988 | Question: 14ii
Consider the following well-formed formula: ... resolution principle that the well-formed formula, given above, cannot be satisfied for any interpretation.
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GATE CSE 1988 | Question: 14i
Consider the following well-formed formula:$\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$Express the above well-formed formula in clausal form.
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GATE CSE 1988 | Question: 13iv
Solve the recurrence equations:$T(n)= T( \frac{n}{2})+1$T(1)=1$
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GATE CSE 1988 | Question: 13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
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GATE CSE 1988 | Question: 13ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
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GATE CSE 1988 | Question: 13ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$f(x)=x^3$, for all $x$ belonging to $G$.
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GATE CSE 1988 | Question: 13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$\overline{G}=G$
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GATE CSE 1988 | Question: 13ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$G$ is the group of non zero real numbers under multiplication.
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GATE CSE 1988 | Question: 12iv
Select SNAME from S Where SNOin (select SNO from SP where PNOin (select PNO from P Where COLOUR='BLUE'))What relations are being used in the above SQL query? Given at least two attributes of each of these relations.
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GATE CSE 1988 | Question: 12iii
Describe the relational algebraic expression giving the relation returned by the following SQL query.Select SNAME from S Where SNOin (select SNO from SP where PNOin (select PNO from P Where COLOUR='BLUE'))
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GATE CSE 1988 | Question: 12iic
Using Armstrong's axioms of functional dependency derive the following rules:$\{ x \rightarrow y, \: z \subset y \} \mid= x \rightarrow z$(Note: $x \rightarrow y$ ... $z$ is subset of $y$, and $\mid =$ means derives).
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GATE CSE 1988 | Question: 12iib
Using Armstrong's axioms of functional dependency derive the following rules:$\{ x \rightarrow y, \: wy \rightarrow z \} \mid= xw \rightarrow z$(Note: $x \rightarrow y$ ... $z$ is subset of $y$, and $\mid =$ means derives).
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GATE CSE 1988 | Question: 12iia
Using Armstrong's axioms of functional dependency derive the following rules:$\{ x \rightarrow y, \: x \rightarrow z \} \mid= x \rightarrow yz$(Note: $x \rightarrow y$ ... $z$ is subset of $y$, and $\mid =$ means derives).
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GATE CSE 1988 | Question: 12i
What are the three axioms of functional dependency for the relational databases given by Armstrong.
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GATE CSE 1988 | Question: 11
A number of processes could be in a deadlock state if none of them can execute due to non-availability of sufficient resources. Let $P_i, 0 \leq i \leq 4$ ... Is the system currently in a safe state? If yes, explain why.
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GATE CSE 1988 | Question: 10iib
Given below is solution for the critical section problem of two processes $P_0$ and $P_1$ sharing the following variables:var flag :array [0..1] of ... . If it is incorrect, demonstrate with an example how it violates the conditions.
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GATE CSE 1988 | Question: 10iia
Translate the executable statements of the following Pascal Program into quadruples. Assume that integer and real values require four words each.repeat flag[i]:=true; while turn !=i do begin ... i:<=10 do begin a[i]:=0; i:=i+1 end; end.
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GATE CSE 1988 | Question: 10ib
Consider the following grammar:$S \rightarrow S$S \rightarrow SS \mid a \mid \epsilon$Indicate the shift-reduce and reduce-reduce conflict (if any) in the various states of the $\text{LR(0)}$ parser.
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GATE CSE 1988 | Question: 10ia
Consider the following grammar:$S \rightarrow S$S \rightarrow SS \mid a \mid \epsilon$Construct the collection of sets of $\text{LR (0)}$ items for this grammar and draw its goto graph.
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GATE CSE 1988 | Question: 9iii
In the program scheme given below indicate the instructions containing any operand needing relocation for position independent behaviour. Justify your answer. ...
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GATE CSE 1988 | Question: 9ii
The code for the implementation of a sub-routine to convert positive numeric data from binary to appropriate character string in a $PDP-11$ like machine has been given belowNote- ...
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GATE CSE 1988 | Question: 9i
The following program fragment was written in an assembly language for a single address computer with one accumulator register:LOAD B MULT C STORE T1 ADD ... MULT T2 ADD T1 STORE ZGive the arithmetic expression implemented by the fragment.
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GATE CSE 1988 | Question: 8iv
Consider the following Ada program:Procedure P is BAD-FORMAT: exception Procedure Q is begin ... if S/='b' then raise BAD-FORMAT end if; ... end Q; Procedure ... 2 end P;Under what conditions are the two handler bodies $1$ and $2$ executed?
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GATE CSE 1988 | Question: 8iii
Write a LISP function to compute the product of all the numbers in a list. Assume that the list contains only number.
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GATE CSE 1988 | Question: 8ii
Consider the two program segments below:for i:=1 to f(x) by 1 do S endi:=1; While i<=f(x) do S i:=i+1 endUnder what conditions are these two programs equivalent? Treat $S$ as any sequence of statements and $f$ as a function.
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GATE CSE 1988 | Question: 8i
Consider the procedure declaration:Procedure P (k: integer)where the parameter passing mechanism is call-by-value-result. Is it correct if the call, P (A ... z;Explain your answer. If this is incorrect implementation, suggest a correct one.
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