Abstract
We discuss some connections between polynomial time and non-uniform, small depth circuits. A connection is shown with simulating deterministic time in small space. The well known result of Hopcroft, Paul and Valiant [HPV77] showing that space is more powerful than time can be improved, by making an assumption about the connection of deterministic time computations and non-uniform, small depth circuits. To be more precise, we prove the following: If every linear time deterministic computation can be done by non-uniform circuits of polynomial size and sub-linear depth, then \(\mathcal{DTIME}(t) \subseteq \mathcal{DSPACE}(t^{1-\epsilon})\) for some constant ε> 0. We can also apply the same techniques to prove an unconditional result, a trade-off type of theorem for the size and depth of a non-uniform circuit that simulates a uniform computation.
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Lipton, R.J., Viglas, A. (2003). Non-uniform Depth of Polynomial Time and Space Simulations. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_29
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DOI: https://doi.org/10.1007/978-3-540-45077-1_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40543-6
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