Section A
Let L € {a, b} * be the language corresponding to the regular expression
bba(ab)*+(ab+ba*b)*ba
Generate the complete CFG for this and convert to CNF
Show the NFA and DFA
Show that the CFG given by
S a | Sa | bSS | SSb | SbS
Is ambiguous.
Describe the “halting problem” for Turing machines.
Prove or disprove that halting problem is undecidable
Consider the language of simple palindromes (with a ‘c’ in the middle position)
SP = { XCX | X € {a , b}*}
What is the least functional FA that can accept this language? Why?
Construct the transition table or the state diagram.
Process the following through the FA and indicate what happens – abcba , acab , and abc
Let L be the language of balanced strings of parentheses, just as they would appear in legal algebraic expression.
Using [ ] as the symbols for the parentheses, show the CFG with its productions.
Show the PDA for part ( a ).
Show the computations trace for [ [ ] [ ] ].
For the language specified by
{ ai bj ck | i >= j or i >= k }
Show that it is a CFL but it is complement is not.
Consider the following two language specifications
L1 = AnBnCn = { an bn cn | n belongs to N the set of natural numbers }
L2 = L = { xcx | x € [ a , b}* }
What kind of FA is required to accept the two language and why?
Show the formal definition for the FA identified in part ( a ) for L1.
Show the transition table for part ( b ).
Section B
Consider two language L1 and L2 defined as follows:
L1 = { x € (a , b) | Where x contains the substring ab }
L2 = { x € (a , b) | Where x contains the substring bba }
Show the state diagram for L1 and L2.
Show the optimal FA accepting L1 U L2.
Design a TM and show the machine diagram that accept the language defined by:
L = { ai baj | 0 <= i < j }
PCP
Describe post’s correspondence problem.
Is post’s correspondence problem solvable? Explain.
Given the following:
A = ( a , abaaa , ab ) and B = ( aaa , ab , b )
As two strings, provide a solution to PCP.
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