MATLAB (must be scripted for MATLAB)

Please see both attached documents for full problem description. Verlet Method. THIS POSTING IS FOR PROBLEM 2.17

MATLAB

In your response, please attach the ".m file" Please see both attached documents for homework specifics. THIS POSTING IS FOR PROBLEM 2.21

Two Dimensional Finite Automaton

1. Define two dimensional finite automaton (2DIM-DFA) is defined as follows. The input is an m X n rectangle, for any m, n  2. The squares along the boundary of the rectangle contain the symbol # and the internal squares contain symbols over the input alphabet . The transition function is a mapping Q x   Q x {L,R,U,D} to indicate the next state and the new head position (Left, Right, Up, down). The machine accepts when it enters one of the designated accept states. It rejects if it tries to move off the input rectangle or if it never halts. Two such machines are equivalent if they accept the same rectangles. Consider the problem of testing whether two ... click for more

Automata

Let  be a 3cnf-formula. An  assignment to the variables of  is one where each clause contains two literals with unequal truth values. In other words an  -assignment satisfies  without assigning three true literals in any clause. a. Show that the negation of any -assignment to  is also an -assignment. b. Let SAT be the collection of 3cnf-formulas that have an -assignment. Show that we obtain a polynomial time reduction from 3SAT to SAT by replacing each clause cI (y1 V y2 V y3) by the two clauses (y1 V y2 V zI) and ( V y3 V b) where zI is a new variable for each clause cI and b is a sin... click for more

Turing Machine

Let B be a probabilistic polynomial time Turing machine and let C be a language where, for some fixed 0 < 1 < 2 < 1, a. w  C implies Pr [B accepts w]  1, and b. w  C implies Pr [B accepts w]  2. Show that C  BPP. HINT: Use Lemma 10.5 to help you find the solution. See attached file for full problem description.