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It is well known that time bounds for machines correspond closely to size bounds for networks, and that space bounds correspond to depth bounds. It is not known whether simultaneous time and space bounds correspond to simultaneous size and depth bounds. It is shown here that simultaneous time and "reversal" bounds correspond to simultaneous size and depth bounds, and that simultaneous time and space bounds correspond to simultaneous size and "width" bounds.
Nicholas Pippenger (Mon,) studied this question.