Computer output, preservation

There are many other possible notions of equivalence, depending on the underlying phenomena one wishes to nodel and study. In our later discussion of block structure and transformations to structured form we shall meet some definitions yet more rigorous than "strong equivalence" - notions of computational equivalence or structure preservation where one demands that not only the end result be the same but that the outputs be obtained in roughly similar ways. One stronger notion is total equivalence which only holds between always halting schemes. 

Bubble logic that implements universal Boolean logic in physical fluid dynamics has been demonstrated in [4]. A bubble traveling in a microchannel can represent a bit of information as well as carry a chemical payload. Therefore, it is possible to integrate chemistry with computation for process control. Since bubble logic preserves the information representation from input to output, devices can be cascaded to implement combinational and sequential Boolean logic. 

A less rigorous but more computationally efficient lower bound on Eq. (1) can be obtained by limiting the space of admissible inputs to sinusoids of varying amplitude and frequency. Provided that the nonlinear system in question preserves periodicity, the output after any transients have decayed can be represented by a Fourier series ... 

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