New Bounds for Energy Complexity of Boolean Functions
Krishnamoorthy Dinesh,Samir Otiv,Jayalal Sarma +2 more
- pp 738-750
TLDR
For a Boolean function f, the energy complexity of C is the maximum over all inputs \(\{0,1\}^n\) the numbers of gates of the circuit C (excluding the inputs) that output a one.Abstract:
For a Boolean function \(f:\{0,1\}^n\rightarrow \{0,1\}\) computed by a circuit C over a finite basis \(\mathcal{B}\), the energy complexity of C (denoted by \(\mathsf {EC}_{\mathcal{B}}(C)\)) is the maximum over all inputs \(\{0,1\}^n\) the numbers of gates of the circuit C (excluding the inputs) that output a one. Energy complexity of a Boolean function over a finite basis \(\mathcal{B}\) denoted by Open image in new window where C is a circuit over \(\mathcal{B}\) computing f.read more
Citations
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Journal ArticleDOI
New bounds for energy complexity of Boolean functions
TL;DR: A parameter positive sensitivity (denoted by psens ), a quantity that is smaller than sensitivity (Cook et al. 1986, [3] ) is defined and shown that for any Boolean circuit C computing a Boolean function f, EC ( C ) ≥ psens ( f ) / 3 .
Journal ArticleDOI
Asymptotically Best Synthesis Methods for Reflexive-Recursive Circuits
TL;DR: Methods are proposed for deriving lower and upper bounds on the Shannon function for the complexity of circuits from classes of reflexive-recursive circuits of bounded depth in an arbitrary basis.
Book ChapterDOI
On the Relationship Between Energy Complexity and Other Boolean Function Measures
TL;DR: In this article, the authors investigated energy complexity, a Boolean function measure related to circuit complexity, and showed that the energy complexity of a function f is the minimum number of activated inner gates over all inputs.
Posted Content
On the Relationship between Energy Complexity and other Boolean Function Measures
TL;DR: This work investigates into energy complexity, a Boolean function measure related to circuit complexity, and affirms the lower bound of the Dinesh, Otiv, and Sarma upper bound on positive sensitivity, which implies the tightness of the two lower bounds of $\mathrm{EC}(f) and $\mathtt{ADDRESS}$ functions.
References
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Book
Computational limitations of small-depth circuits
TL;DR: The techniques described in "Computational Limitations for Small Depth Circuits" can be used to demonstrate almost optimal lower bounds on the size of small depth circuits computing several different functions, such as parity and majority.
Journal ArticleDOI
Upper and lower time bounds for parallel random access machines without simultaneous writes
TL;DR: It is shown that even if the authors allow nonuniform algorithms, an arbitrary number of processors, and arbitrary instruction sets, $\Omega (\log n)$ is a lower bound on the time required to compute various simple functions, including sorting n keys and finding the logical “or” of n bits.
Book
Boolean Function Complexity: Advances and Frontiers
TL;DR: In this article, a comprehensive description of basic lower bound arguments, covering many of the gems of this complexity Waterloo that have been discovered over the past several decades, right up to results from the last year or two, is given.
Journal ArticleDOI
On the Inversion Complexity of a System of Functions
TL;DR: The alphabet is called an alphabet of a formula in n variables words in the alphabet,I)~ which is defined by the following generating rules.
Proceedings ArticleDOI
Shrinkage of De Morgan Formulae by Spectral Techniques
TL;DR: A new and improved proof that the shrinkage exponent of De Morgan formulae is 2 is given, and for any Boolean function f, setting each variable out of x1,.. . , xn with probability 1 - p to a randomly chosen constant, reduces the expected formula size of the function by a factor of O(p2).