Q2. What is the time required for the operation of this analog computer?
The time required for the operation of this analog computer will depend on the parasitic capacitance of the circuit, which will determine the effective RC time constant of the circuit.
Q3. What is the rule of simulation that Feynman wants to have?
He says:‘‘The rule of simulation that The authorwould like to have is that the number of computer elements required to simulate a large physical system is only to be proportional to the space-time volume of the physical system.
Q4. What is the optimum solution of (5.1)?
Since the angular positions x 1 and x 2 always satisfy the constraints imposed by the stops, the maximum angular position of the z shaft will be the optimum solution of (5.1).
Q5. What is the volume of the corresponding sphere in p-dimensional space?
If the norm of f(x) is bounded by the polynomial L k , the volume of the corresponding sphere in p-dimensional space is O(L pk ) .
Q6. What is the proof of convergence for this kind of stochastic relaxation algorithm?
a proof of convergence for this kind of stochastic relaxation algorithm has only been obtained under the assumption of an annealing schedule involving logarithmically decreasing temperature [10]; the resulting algorithm requires exponential time which is in agreement with their prediction based on assuming Strong Church’s Thesis and P ≠ NP.
Q7. What is the maximum magnitude of the second derivative of the solution vector over the interval?
The maximum magnitude of the second derivative of the solution vector over the interval [t 0 ,t f ] , is used as a measure of the resources required by the computation.
Q8. What is the equivalence class of the output vector?
The solution at time t f when the initial condition at time t 0 is y 0 and the precision constant ε determine an equivalence class of ‘‘output’’ vectors.
Q9. What is the way to solve the problem of finding a minimum-length interconnection network?
In [18] the problem of finding a minimum-length interconnection network between given points in the plane is solved with movable and fixed pegs interconnected by strings; a locally optimal solution is obtained by pulling the strings.
Q10. What is the model for a well-defined digital computer?
Turing has laid out a model for what a well-defined digital computation must be: it uses a finite set of symbols (without loss of generality {0,1}) to store information, it can be in only one of a finite set of states, and it operates by a finite set of rules for moving from state to state.
Q11. What is the restriction for encoding the value of a variable x?
A ‘‘physical digital computer’’ would allow encoding the value n for the variable x with k = O(logn) distinct electric fields, shaft angles, etc.
Q12. What is the argument for using analog computers?
The authors would argue that for the purposes of investigating the limitations on analog computation arising from computational complexity theory, the use of ‘‘idealized’’ analog computers whose physical operation corresponds precisely to its mathematical description is appropriate.
Q13. How many edges will be a good representation of the capacitance?
If the wire lengths grow linearly with the number of edges | E|, the total capacitance seen by the voltage source will be no worse than proportional to | E| 2 .