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Computer Science, Data Structures and Algorithms
Year 1
Automata and Computability
A Boolean formula is a Boolean circuit wherein every gate has only one output wire. The same input variable may appear in multiple places of a Boolean formula. Prove that a language has a polynomial size family of formulas if it is in NC1. Ignore uniformity considerations.
See attached file for full problem description.
Problem A145.doc View File
By OTA: Rajender Kumar, MCom
OTA Rating: 4.8/5
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Automata and Computability - Show that the problem of testing whether two branching programs compute the same function is solvable in polynomial time if and only if P = NP
Automata and Computability - Give a circuit that computes the parity function on three input variables and show how it computes on input 011.
See attached file for full problem description.
Automata and Computability - Recall that we may consider circuits that output strings over {0,1} by designating several output gates. Let addn: {0,1}2n{0,1}n+1 take the sum of two n bit binary integers and produce the n + 1 bit result. Show that we can compute the addn function with 0(n) size circuits.
See attached file for full problem description.
Automata and Computability - Prove that, if A is a regular language, a family of family programs B1, B2, … exists wherein each Bn accepts exactly the strings in A of length n and is bounded in size by a constant times n.
See attached file for full problem description.
Automata and Computability (A18) - See Attached Question Sheet and Theorem Sheet
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