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

Recall that NPSAT is the class of languages that are recognized by nondeterministic polynomial time Turing machines with an oracle for the satisfiability problem. Show that NPSAT = 2P. 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

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

Create an application that will allow the user to input a matrix of three columns and four rows

The input must be done though text boxes. By default, the array must have the following values: 5, 2, 3 8, 32, 1 4, 9, 10 17, 15, 12 The application will multiply the columns of the matrix (e.g., 5 * 8 * 4 * 17 = 2720) and subtract the rows (e.g., 5 – 2 – 3 = 0). Display the results for the multiplication of all columns and the subtraction of all rows in a message box. Create a menu bar with a Calculate menu and include a Compute and an Exit command. The Compute command will calculate either the multiplication or the subtraction of the rows or columns in the array. Create a Clear button that will clear the result text box and reset all controls. Create an Exit button. Use... click for more