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SPRING 2016 , ASSIGNMENT
PROGRAM MCA(REVISED FALL 2007)
SUBJECT CODE & NAME MC0082- THEORY OF COMPUTER SCIENCE
SEMESTER 5TH SEM
CREDITS 4
MAX. MARKS 60
BK ID B0970
Answer all questions
1 Differentiate between Recursive Functions and growth functions.
Answer : What's a Recursive Function?
Technically,arecursive functionisa functionthatmakesa call to itself.Topreventinfiniterecursion,
youneedan if-elsestatement(of some sort) whereone branchmakesarecursive call,and the other
branch does not. The branch without a recursive call is usually the base case (base cases do not
make recursive calls to the function).
Functionscanalso be mutuallyrecursive.Forexample,functionf() can call function g() and function
g() can call function f(). This is still considered re
2. Describe direct and indirect proof techniques.
Ans : Direct proof :
In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given
statement by a straightforward combination of established facts, usually existing lemmas and
theorems, without making any further assumptions. In order to directly prove a conditional
statementof the form"If p, thenq", itsufficestoconsiderthe situationsinwhich the statement p is
true. Logical deduction is employed to reason from assumptions to conclusion. The type of logic
employed is almost invariably first-order
3. Discuss about Walks and Paths in Trees
Ans : Walks and Paths in Trees :

2. In the mathematical field of graph theory, a path graph or linear graph is a particularly simple
example of a tree, namely a tree with two or more vertices that is not branched at all, that is,
containsonlyverticesof degree 2and1. In particular,ithas twoterminal vertices(verticesthathave
degree 1), while all others (if any) have degree 2.
A pathin a graph isa sequence of verticessuchthatfrom each of its vertices there is an edge to the
next vertex in the sequence. A path may
4. What is DFA? Discuss about Transition System.
Ans : DFA :
In automata theory, a branch of theoretical computer science, a deterministic finite automaton
(DFA)—also known as deterministic finite state machine—is a finite state machine that
accepts/rejects finite strings of symbols and only produces a unique computation (or run) of the
automaton for each input string.'Deterministic' refers to the uniqueness of the computation. In
searchof simplestmodelstocapture the finite state machines,McCullochandPittswere among the
first researchers to introduce a concept similar to finite automaton in 1943.
The figure on the right illustrates a
5. Differentiate between Moore machine and Mealy machine.
Ans : Moore machine :
In the theory of computation, a Moore machine is a finite-state machine whose output values are
determinedsolely by its current state. This is in contrast to a Mealy machine, whose output values
are determined both by its current state and by the values of its inputs. The Moore machine is
namedafterEdwardF. Moore, whopresentedthe conceptin a1956 paper,“Gedanken-experiments
on Sequential Machines.
A Moore machine can be defined as a 6-tuple ( S, S0, Σ, Λ, T, G ) consisting of the following:
a finite set of states ( S )
6. Define context-free grammar. What is an ambiguous grammar? Explain with an example.
Ans : Ambiguous grammer :
In computerscience,anambiguousgrammarisa formal grammar forwhichthere existsa string that
can have more than one leftmost derivation, while an unambiguous grammar is a formal grammar
for whicheveryvalidstringhasaunique leftmostderivation.Manylanguagesadmitbothambiguous
and unambiguous grammars, while some languages admit only ambiguous grammars. Any non-
empty language admits an ambiguous
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