Abstract
In this paper we ask, “Can anything be said about a smallest circuit that computes a given function.” We are able to show that for a wide class of functions, which includes all graph problems, an optimal circuit has a restricted structure. For instance, the input wires in an optimal circuit for Hamiltonian Path have at most linear fan-out. This is analogous to the possibly counter-intuitive statement that there is a straight line program for Hamiltonian Path on graphs with n nodes that looks at each edge only O(n 2) times.
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Bibliography
R. B. Boppana, Threshold Functions and Rounded Depth Monotone Circuits, ACM SIGACT 16(1984), 475–479.
R. Fagin, M. M. Klawe, N. J. Pippenger, L. Stockmeyer. Bounded depth. polynomial-size circuits for symmetric functions, IBM Research Report RI 4040. Oct. 1983.
M. Furst, J. B. Saxe, and M. Sipser, Parity, Circuits, and the Polynomial Time Hierarchy, IEEE FOCS 22(1981) 260–270.
W. J. Paul, Realizing Boolean Functions on Disjoint Sets of Variables. Theoretical Computer Science 2(1976) 383–396.
R. Smolensky, Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity, ACM SIGACT 19(1987).
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© 1988 Springer-Verlag Berlin Heidelberg
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Rudich, S., Berman, L. (1988). Optimal circuits and transitive automorphism groups. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_138
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DOI: https://doi.org/10.1007/3-540-19488-6_138
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