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

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...

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Veröffentlicht in:Theoretical computer science Jg. 237; H. 1; S. 197 - 212
Hauptverfasser: Sengupta, Rimli, Venkateswaran, H.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 28.04.2000
Elsevier
Schlagworte:
Algebraic logic
Boolean circuit
Cancellation
Combinatorics
Combinatorics. Ordered structures
Complexity classes
Determinant
Exact sciences and technology
Graph theory
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Monotonicity
Sciences and techniques of general use
Cancellation
Boolean circuit
Determinant
Monotonicity
Complexity classes
Boolean logic
Completeness
Boolean function
Graph theory
Boolean algebra
Complexity
ISSN:0304-3975, 1879-2294
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Zusammenfassung: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 NP and circuit definable classes above it remain unchanged.
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(98)00170-4