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Deterministic restrictions in circuit complexity

1996
*
Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96
*

log n))), showing that it is not possible to simultaneously optimize the number of gates and wires

doi:10.1145/237814.237824
dblp:conf/stoc/ChaudhuriR96
fatcat:ygv5jr7cwndlngr6m3t2y6pffm
*in*a threshold*circuit*. ... We give*circuit*constructions that show that the bound O(S 1− (d) ) is near optimal. We also study the*complexity*of computing threshold functions. ... Acknowledgment We are grateful to Mike Paterson and Uri Zwick for helpful discussions and for pointing us to the work*in*[2] . ...##
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A Note on the Power of Non-Deterministic Circuits with Gate Restrictions
[article]

2017
*
arXiv
*
pre-print

We investigate the power of non-

arXiv:1705.03263v2
fatcat:allsln2k2fbcbnfsop3oh277py
*deterministic**circuits*over*restricted*sets of base gates. ... We note that the power of non-*deterministic**circuits*exhibit a dichotomy,*in*the following sense: For weak enough bases, non-*deterministic**circuits*are no more powerful than*deterministic**circuits*, and ...*complexity*, but does not have polynomial*deterministic*G-*circuit**complexity*. ...##
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Parameterized Analogues of Probabilistic Computation
[article]

2014
*
arXiv
*
pre-print

Our definition uses the machine based characterization of the parameterized

arXiv:1409.7790v1
fatcat:asy7frwdinhafnd33l2hewxoo4
*complexity*class W[P] obtained by Chen et.al [TCS 2005]. ... We study a parameterization of the polynomial identity testing problem based on the degree of the polynomial computed by the arithmetic*circuit*. ... Acknowledgements We thank anonymous reviewers for their comments on an earlier version of this paper which helped*in*improving the presentation of the article. ...##
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On Relating Time and Space to Size and Depth

1977
*
SIAM journal on computing (Print)
*

*circuit*

*complexity*. ... Turing machine space

*complexity*is related to

*circuit*depth

*complexity*. ... Relating open problems

*in*Turing machine and

*circuit*

*complexity*. ...

##
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Parameterized Analogues of Probabilistic Computation
[chapter]

2015
*
Lecture Notes in Computer Science
*

Our definition uses the machine based characterization of the parameterized

doi:10.1007/978-3-319-14974-5_18
fatcat:73zawyw5trftjgkbpbpjkr6vbe
*complexity*class W[P] obtained by Chen et.al [TCS 2005]. ... We study a parameterization of the polynomial identity testing problem based on the degree of the polynomial computed by the arithmetic*circuit*. ... Acknowledgements We thank anonymous reviewers for their comments on an earlier version of this paper which helped*in*improving the presentation of the article. ...##
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Page 4494 of Mathematical Reviews Vol. , Issue 87h
[page]

1987
*
Mathematical Reviews
*

The authors show that

*deterministic*Turing machines with alternating Turing machines as oracles under par- ticular resource bounds (the space*complexity*is not greater than log |z| and alternation*complexity*—the ... We study*restrictions*R on both the*deterministic*and also the nondeterministic polynomial time- bounded oracle machines such that the following holds: P = NP if and only if, for every set A, Pp(A) = NPr ...##
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The power of nondeterminism in polynomial- size bounded-width branching programs

1988
*
Theoretical Computer Science
*

Nondeterministic branching programs introduced by Meinel (1986) proved to be an interesting computational tool for describing higher

doi:10.1016/0304-3975(88)90073-4
fatcat:6vjzkxcfijeyxes3x4ilwsmk7a
*complexity*classes (Meinel 1988). ... Investigation of the power of nondeterminism*in*the case of bounded-width nondeterministic branching programs yields the following results: (i) I-time-only-nondeterministic, polynomial-size, and bounded-width ...*circuits*or branching programs than to*complex*types of Turing machines,*circuit*-based characterizations of*complexity*classes gain more and more importance. ...##
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Limiting negations in non-deterministic circuits

2009
*
Theoretical Computer Science
*

*In*this paper, we consider

*circuits*computing non-

*deterministically*and determine the inversion

*complexity*of every Boolean function. ... The minimum number of NOT gates

*in*a Boolean

*circuit*computing a Boolean function f is called the inversion

*complexity*of f . ... I especially thank one of the referees who pointed out that the result

*in*the early version could be extended to the one

*in*Section 3.2. ...

##
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Some Results on the Circuit Complexity of Bounded Width Circuits and Nondeterministic Circuits
[article]

2019
*
arXiv
*
pre-print

We prove that there is a Boolean function f such that the nondeterministic U_2-

arXiv:1811.01347v2
fatcat:lqgvw3i2pnbfrmv5tt4cjlk6fu
*circuit**complexity*of f is at most 2n + o(n) and the*deterministic*U_2-*circuit**complexity*of f is 3n - o(n). ...*In*the third part of this paper, we show a relation between*deterministic*bounded width*circuits*and nondeterministic bounded width*circuits*. ... While both of nondeterministic computation and*circuit**complexity*are central topics*in*computational*complexity*, the*circuit**complexity*of nondeterministic*circuits*is relatively not well studied. ...##
###
Hardness as randomness: a survey of universal derandomization
[article]

2003
*
arXiv
*
pre-print

*In*fact, proving that probabilistic algorithms have non-trivial

*deterministic*simulations is basically equivalent to proving

*circuit*lower bounds, either

*in*the algebraic or Boolean models. ... We survey recent developments

*in*the study of probabilistic

*complexity*classes. ... Either no problem

*in*E has strictly exponential

*circuit*

*complexity*or P = BP P . ...

##
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Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

2019
*
Quantum
*

Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum

doi:10.22331/q-2019-07-11-162
fatcat:po75rwjtkfcrzgr2iock3f3fwi
*circuits*. ... We establish a*deterministic*polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. ... QUANTUM SIMULATION*Complex*-valued Ising model partition functions arise naturally*in*the output probability amplitudes of quantum*circuits*[1, 22] . ...##
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Lower Bounds for the Size of Nondeterministic Circuits
[chapter]

2015
*
Lecture Notes in Computer Science
*

Nondeterministic

doi:10.1007/978-3-319-21398-9_23
fatcat:jjmv7xontveqvh37wxdnkvuimq
*circuits*are a nondeterministic computation model*in**circuit**complexity*theory. ... We also discuss an approach to proving lower bounds for the size of*deterministic**circuits*via lower bounds for the size of nondeterministic*restricted**circuits*. ... Introduction Proving lower bounds for the size of Boolean*circuits*is a central topic*in**circuit**complexity*theory. ...##
###
Lower Bounds for the Size of Nondeterministic Circuits
[article]

2015
*
arXiv
*
pre-print

Nondeterministic

arXiv:1504.06731v1
fatcat:tmblthyjsrh5xcnfh7r4h3emvm
*circuits*are a nondeterministic computation model*in**circuit**complexity*theory. ... We also discuss an approach to proving lower bounds for the size of*deterministic**circuits*via lower bounds for the size of nondeterministic*restricted**circuits*. ... Introduction Proving lower bounds for the size of Boolean*circuits*is a central topic*in**circuit**complexity*theory. ...##
###
Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs
[article]

2018
*
arXiv
*
pre-print

Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum

arXiv:1806.11282v1
fatcat:cyuqsil4bbe2ffzcscupsis26a
*circuits*. ... We establish a*deterministic*polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. ... QUANTUM SIMULATION*Complex*-valued Ising model partition functions arise naturally*in*the output probability amplitudes of quantum*circuits*[1, 19] . ...##
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On the Computational Power of Radio Channels

2019
*
International Symposium on Distributed Computing
*

Using techniques from

doi:10.4230/lipics.disc.2019.8
dblp:conf/wdag/BravermanKOT19
fatcat:ezmqszklgbculk6ywmvifyreh4
*circuit**complexity*, we show that*in*many cases, the answer is "no". ... Next, we use the technique of random*restrictions*, used to prove AC 0 lower bounds, to prove a tight lower bound of Ω(1/ 2 ) on computing a (1 ± )-approximation to the sum of the nodes' inputs. ... To do so, we use another classical technique from*circuit**complexity*, called random*restrictions*(defined*in*Subsection 4.2). ...
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