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Abstract: For a monoid G, the iterated multiplication problem is the computation of the product of n elements from G. By refining known completeness arguments, we show that as G varies over a natural series of important groups and monoids, the iterated multiplication problems are complete for most natural, low-level complexity classes. The completeness is with respect to "first-order projections" -- low-level reductions that do not obscure the algebraic nature of these problems. 1 Introduction In recent ... (Update)
Context of citations to this paper: More
.... is logspace uniform, given access to the product of the first n primes, and thus that the full construction is TC uniform [40]. There has also been work reducing the size and depth of division circuits. Division circuits of depth O(log n) and size n were presented in...
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BibTeX entry: (Update)
N. Immerman and S. Landau. The complexity of iterated multiplication. Information and Computation, 116:103--116, 1995. http://citeseer.ist.psu.edu/immerman95complexity.html More
@inproceedings{ immerman89complexity,
author = "Neil Immerman and Susan Landau",
title = "The Complexity of Iterated Multiplication",
booktitle = "Structure in Complexity Theory Conference",
pages = "104-111",
year = "1989",
url = "citeseer.ist.psu.edu/immerman95complexity.html" }
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370 A Mathematical Introduction to Logic (context) - Enderton - 1972
211 Languages That Capture Complexity Classes - Immerman - 1987 ACM DBLP
170 Nondeterministic Space is Closed Under Complementation - Immerman - 1988 ACM DBLP
168 A Taxonomy of Problems with Fast Parallel Algorithms (context) - Cook - 1985 ACM DBLP
125 On Uniform Circuit Complexity (context) - Ruzzo - 1981 DBLP
91 Log Depth Circuits for Division and Related Problems (context) - Beame, Cook et al. - 1986 ACM DBLP
61 Descriptive and Computational Complexity - Immerman - 1989 ACM DBLP
60 On Computing Determinant in Small Parallel Time Using a Smal.. (context) - Berkowitz - 1984
51 On Threshold Circuits and Polynomial Computation - Reif - 1987 ACM DBLP
45 Expressibility and Parallel Complexity - Immerman - 1989 ACM DBLP
44 the Computational Power of PP and \PhiP (context) - Toda - 1989
43 Bounded-Width Polynomial-Size Branching Programs Recognize E.. (context) - Barrington - 1989
42 The Method of Forced Enumeration for Nondeterministic Automa.. (context) - Szelepcs'enyi - 1988 ACM DBLP
29 Problems Complete for Deterministic Logarithmic Space (context) - Cook, McKenzie - 1987 ACM DBLP
27 Extensions to Barrington 's M-program model - B'edard, Lemieux et al. - 1990
25 Structure and Importance of Logspace-MOD Class (context) - Buntrock, Damm et al. - 1992 DBLP
23 Reducibility By Algebraic Projections (context) - Valiant - 1982
21 Uniform Circuit Complexity (context) - Allender - 1989
18 On Uniformity Within NC 1 (context) - Barrington, Immerman et al. - 1990
17 Reduction to NP-Complete Problems by Interpretations (context) - Dahlhaus - 1984 ACM DBLP
15 Computing Algebraic Formulas Using A Constant Number of Regi.. (context) - Ben-Or, Cleve - 1992 ACM DBLP
14 A First-Order Isomorphism Theorem - Allender, Immerman et al. - 1993 ACM DBLP
11 One-Way Log Tape Reductions (context) - Hartmanis, Immerman et al. - 1978
11 A Purely Logical Characterization of Circuit Uniformity (context) - Lindell - 1992 DBLP
11 The Power of the Middle Bit (context) - Green, Kobler et al. - 1992 DBLP
10 Juris Hartmanis: Fundamental Contributions to Isomorphism Pr.. (context) - Young - 1990
3 Isomorphisms and 1-L Reductions (context) - Allender - 1988 ACM DBLP
3 Using the Hamiltonian Operator to Capture NP (context) - Stewart - 1992
2 Some Remarks on Generalized Spectra (context) - Lov'asz, G'acs - 1977
1 On Polynomial Time Isomorphisms of Complete Sets (context) - Berman, Hartmanis - 1977 ACM DBLP
1 th Structure in Complexity Theory Symp (context) - Beaudry, McKenzie et al. - 1992
1 A Note on the Determinant and Permanent Problem (context) - Cai - 1990 ACM DBLP
1 Reducibility Among Combinatorial Problems in Log n Space (context) - Jones - 1973
1 The Complexity of Theorem (context) - Cook - 1971
1 Permanent and Determinant (context) - Gathen - 1987 DBLP
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