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Deterministic restrictions in circuit complexity

Shiva Chaudhuri, Jaikumar Radhakrishnan
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 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] .  ... 
doi:10.1145/237814.237824 dblp:conf/stoc/ChaudhuriR96 fatcat:ygv5jr7cwndlngr6m3t2y6pffm

A Note on the Power of Non-Deterministic Circuits with Gate Restrictions [article]

Gustav Nordh
2017 arXiv   pre-print
We investigate the power of non-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.  ... 
arXiv:1705.03263v2 fatcat:allsln2k2fbcbnfsop3oh277py

Parameterized Analogues of Probabilistic Computation [article]

Ankit Chauhan, B. V. Raghavendra Rao
2014 arXiv   pre-print
Our definition uses the machine based characterization of the parameterized 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.  ... 
arXiv:1409.7790v1 fatcat:asy7frwdinhafnd33l2hewxoo4

On Relating Time and Space to Size and Depth

Allan Borodin
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.  ... 
doi:10.1137/0206054 fatcat:f45h6aubu5br3cgwhdz2t6nnp4

Parameterized Analogues of Probabilistic Computation [chapter]

Ankit Chauhan, B. V. Raghavendra Rao
2015 Lecture Notes in Computer Science  
Our definition uses the machine based characterization of the parameterized 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.  ... 
doi:10.1007/978-3-319-14974-5_18 fatcat:73zawyw5trftjgkbpbpjkr6vbe

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  ... 

The power of nondeterminism in polynomial- size bounded-width branching programs

Christoph Meinel
1988 Theoretical Computer Science  
Nondeterministic branching programs introduced by Meinel (1986) proved to be an interesting computational tool for describing higher 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.  ... 
doi:10.1016/0304-3975(88)90073-4 fatcat:6vjzkxcfijeyxes3x4ilwsmk7a

Limiting negations in non-deterministic circuits

Hiroki Morizumi
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.  ... 
doi:10.1016/j.tcs.2009.05.018 fatcat:uf6mrjlounhm5a5yxpqbxw4mce

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

Hiroki Morizumi
2019 arXiv   pre-print
We prove that there is a Boolean function f such that the nondeterministic U_2-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.  ... 
arXiv:1811.01347v2 fatcat:lqgvw3i2pnbfrmv5tt4cjlk6fu

Hardness as randomness: a survey of universal derandomization [article]

Russell Impagliazzo
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 .  ... 
arXiv:cs/0304040v1 fatcat:vp2asft6sbcxvom7jwth43me7e

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

Ryan L. Mann, Michael J. Bremner
2019 Quantum  
Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum 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] .  ... 
doi:10.22331/q-2019-07-11-162 fatcat:po75rwjtkfcrzgr2iock3f3fwi

Lower Bounds for the Size of Nondeterministic Circuits [chapter]

Hiroki Morizumi
2015 Lecture Notes in Computer Science  
Nondeterministic 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.  ... 
doi:10.1007/978-3-319-21398-9_23 fatcat:jjmv7xontveqvh37wxdnkvuimq

Lower Bounds for the Size of Nondeterministic Circuits [article]

Hiroki Morizumi
2015 arXiv   pre-print
Nondeterministic 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.  ... 
arXiv:1504.06731v1 fatcat:tmblthyjsrh5xcnfh7r4h3emvm

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs [article]

Ryan L. Mann, Michael J. Bremner
2018 arXiv   pre-print
Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum 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] .  ... 
arXiv:1806.11282v1 fatcat:cyuqsil4bbe2ffzcscupsis26a

On the Computational Power of Radio Channels

Mark Braverman, Gillat Kol, Rotem Oshman, Avishay Tal, Michael Wagner
2019 International Symposium on Distributed Computing  
Using techniques from 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).  ... 
doi:10.4230/lipics.disc.2019.8 dblp:conf/wdag/BravermanKOT19 fatcat:ezmqszklgbculk6ywmvifyreh4
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