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Abstract: Counting is AC -reducible to the graph of multiplication. Hence the graph of multiplication is equivalent under AC reductions to majority and to the function form of multiplication. (Update)
Context of citations to this paper: More
...advantage of inspecting all the bits of z, the putative product. An easy reduction in [FSS84] shows MULT ## AC 0 , but is was not until [Bu92] that DMULT ## AC 0 was proved. A simple argument [We94] shows that computing DMULT with read once programs is as hard as factoring:...
.... is hard for syntactic nondeterministic read k times branching programs [12] Note that DMULT function is AC equivalent to MULT [9]. Our result answers also to the open problem raised in [22] about succinct representations for functions DMULT and MULT . We recall now...
Cited by: More
VTC0: A Second-Order Theory for TC0 - Nguyen, Cook (Correct)
Theories for Complexity Classes and their Propositional Translations - Cook (2004) (Correct)
Restricted Branching Programs and Hardware Verification - Ponzio (1995) (Correct)
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0.4: Lower Bounds For Uniform Constant Depth Circuits - Gore (1993) (Correct)
0.4: Bounded Arithmetic, Proof Complexity and Two Papers of Parikh - Buss (2002) (Correct)
0.1: On Uniformity Within NC 1 - Barrington, Immerman, Straubing (1990) (Correct)
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0.1: Resource-bounded Continuity and Sequentiality for Type-two.. - Buss, al. (Correct)
0.1: Some Remarks on Lengths of Propositional Proofs - Buss (Correct)
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6: the complexity of VLSI implementations and graph representations of Boolean func.. - Bryant - 1991
6: On Lower Bounds for Read-k-times Branching Programs (context) - Borodin, Razborov et al. - 1993
6: Symbolic boolean manipulation with ordered binary decision diagrams - Bryant - 1992
BibTeX entry: (Update)
R. Buss, The graph of multiplication is equivalent to counting, Information Processing Letters, 41, (1992), 199-201. http://citeseer.ist.psu.edu/buss91graph.html More
@article{ buss92graph,
author = "Samuel R. Buss",
title = "The Graph of Multiplication is Equivalent to Counting",
journal = "Information Processing Letters",
volume = "41",
number = "4",
pages = "199-201",
year = "1992",
url = "citeseer.ist.psu.edu/buss91graph.html" }
Citations (may not include all citations):116 On uniformity within NC - Barrington, Immerman et al. - 1990
103 Bounded Arithmetic (context) - Buss
92 Constant depth reducibility (context) - Chandra, Stockmeyer et al. - 1984
55 circuits and the polynomial-time hierarchy (context) - Furst, Saxe et al. - 1984
10 Model theoretic aspects of computational complexity (context) - Lipton - 1978
3 Applications of complexity theory to # 0 -definability probl.. (context) - Wilkie - 1979
1 Sharply bounded predicates do not exhaust the polynomial tim.. (context) - Mancivi - 1990
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