Exercise $1\mathrm{.}3$ Draw a deterministic state machine and a non$-$deterministic state machine, with at least five states.

Exercise $1\mathrm{.}4$ Draw a reversible state machine and an irreversible state machine, with at least five states.

Exercise $1\mathrm{.}5$ The following Mathematica code generates a graphical representation of the behaviour of a Cellular Automaton associated with Rule $30.$

ArrayPlot $[$CellularAutomaton $[30,\{\{1\},0\},100]$

The state update rule is visualized using

RulePlot $[$CellularAutomaton $[30]]$

Explain how this update rule, in conjunction with a sequence of filled and blank cells, defines a infinite state machine. Then explain how altering the update rule corresponds to a different state machine.

Exercise $1\mathrm{.}6$ Show that Classical Mechanics is deterministic, then determine the conditions under which Classical Mechanics is reversible.

Exercise $1\mathrm{.}7$ Show that Newton's Second Law of Motion is invariant under Gallinean transformations, and a constant force.