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Let the following problem ALLCFG: Given CFG G, is L(G) = Σ*? This problem is undecidable. (You do not have to prove this).
(a) Is this problem in RE (class of recursively enumerable languages), in core (class of all languages whose complement is in RE), in both, or in neither? Describe your answer.
(b) Use undecidability of ALLCFG to illustrate that following problem is also undecidable: Given PDA M1 and FA M2, is L(M1) = L(M2)?
Write down the grammar for language comprising of strings which have n copies of letter a followed by same number of copies of letter b, where n > 0.
We showed to prove that if L can be identified by DFA then the language left half(L) = {x ∈ ∑*|∃y xy ∈ L and |x| = |y|} is also regular; here |x| means length of x.
In this problem, we consider a very restricted subset of Boolean expressions. Define an operator to be one of the four symbols: ¬, ∧, ∨, and →. Define a variable to be one of the five symbols
Consider the following grammar: S S (S) | ε. Construct and DFA or LR(0) items for this grammar. Construct SLR(1) parsing table.
Express the given correctness properties in LTL. Defne propositions/variables to model the events mentioned in the question. If a parent process calls the blocking waitpid() system call then it is blocked until child process terminates.
Describe the difference between a Deterministic Finite Automata and Non-Deterministic Finite Automata. In general, which one is expected to have less number of states ?
Use any algorithm we without writing out details of algorithm. In proving problem NP-complete, you may utilize NP completeness of any of the problems.
Create a Mealy Machine which produces the output of 1 whenever discrepancy in above pattern is detected, and produces the output of 0 otherwise. Write states meaningful names.
Provide DFA's accepting the following languages over alphabet {0,1}. Set of all strings that, when interpreted as the binary integer, is a multiple of 5.
Discuss the difference between the front end and back-end processes of office automation? Provide some examples in your workplace or that you come into contact with?
Show that the following identities hold for regular expressions over any alphabet: epsilon + R*R = R*. These should be done by interpreting the regular expressions as languages.
Give a construction that assumes you are given a DFA for L and show how to construct an NFA (with or without ε-moves) to recognize sort(L).
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