  By considering a discrete tape where each cell corresponds to an integer,
thus to a possible sum, a pseudo-polynomial solution can be given to subset sum
problem, which is an NP-complete problem and a cornerstone application for this
study, using shifts and element-wise summations. This machinery can be extended
symbolically to continuous case by thinking each possible sum as a single
frequency impulse on the frequency band. Multiplication with a cosine in this
case corresponds to the shifting operation as modulation in communication
systems. Preliminary experimentation suggests that signal generation thus
solution space calculation can be done in polynomial time. However, reading the
value at a specific frequency (sum value) is problematic, namely cannot be
simulated in polynomial time currently. Dedicated hardware implementation might
be a solution, where both circuit-based and wireless versions might be tried
out. A polynomial representation is also given that is claimed to be analogous
to a tape of a Turing machine. Both rational and real number versions of the
subset sum problem are also discussed, where the rational version of the
problem is mapped to 0-1 range with specific patterns of True values. Although
this machinery may not be totally equivalent to a non-deterministic Turing
machine, it may be helpful for non-deterministic universal Turing machine
actualization. It may pave way to both theoretical and practical considerations
that can help computing machinery, information processing, and pattern
recognition domains in various ways.
