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Abstract: Cancellations are known to be helpful in efficient algebraic computation of polynomials over fields. We define a notion of cancellation in Boolean circuits and define Boolean circuits that do not use cancellation to be non-cancellative. Non-cancellative Boolean circuits are a natural generalization of monotone Boolean circuits. We show that in the absence of cancellation, Boolean circuits require super-polynomial size to compute the determinant interpreted over GF(2). This non-monotone... (Update)
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BibTeX entry: (Update)
@article{ sengupta00noncancellative,
author = "Rimli Sengupta and H. Venkateswaran",
title = "Non-cancellative {Boolean} circuits: {A} generalization of monotone {Boolean} circuits",
journal = "Theoretical Computer Science",
volume = "237",
number = "1--2",
pages = "197--212",
year = "2000",
url = "citeseer.ist.psu.edu/295589.html" }
Citations (may not include all citations):83 The monotone circuit complexity of Boolean functions (context) - Alon, Boppana - 1987
52 A very hard log space counting class (context) - Alvarez, Jenner - 1990
48 Two applications of inductive counting for complementation p.. (context) - Borodin, Cook et al. - 1989
26 Monotone versus positive (context) - Ajtai, Gurevich - 1987
25 Structure and importance of the logspaceMOD class (context) - Buntrock, Damm et al. - 1992
19 Superpolynomial lower bounds for monotone span programs - Babai, Gal et al. - 1996
13 Monotone separation of Logspace from NC (context) - Grigni, Sipser
5 A catalogue of complexity classes (context) - Johnson - 1990
2 Structure in monotone complexity - Grigni - 1991
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