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 - 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 - 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.

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