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Non-cancellative Boolean circuits: A generalization of monotone Boolean circuits

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1180))

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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 Boolean function is known to be in P. In the spirit of monotone complexity classes, we define complexity classes based on non-cancellative Boolean circuits. We show that when the Boolean circuit model is restricted by withholding cancellation, P and popular classes within P are restricted as well, but classes NP and above remain unchanged.

This work was supported by NSF grant CCR-9200878 and was done while the first author was at the College of Computing, Georgia Tech.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Rose-Hulman Institute of Technology, 47803-3999, Terre Haute, IN

    Rimli Sengupta

  2. College of Computing, Georgia Institute of Technology, 30332-0280, Atlanta, GA

    H. Venkateswaran

Authors
  1. Rimli Sengupta
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  2. H. Venkateswaran
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Editor information

V. Chandru V. Vinay

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© 1996 Springer-Verlag Berlin Heidelberg

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Sengupta, R., Venkateswaran, H. (1996). Non-cancellative Boolean circuits: A generalization of monotone Boolean circuits. In: Chandru, V., Vinay, V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1996. Lecture Notes in Computer Science, vol 1180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62034-6_58

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  • DOI: https://doi.org/10.1007/3-540-62034-6_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62034-1

  • Online ISBN: 978-3-540-49631-1

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