scholarly journals Simulating Boolean circuits on a DNA computer

1997 ◽  
Author(s):  
Mitsunori Ogihara ◽  
Animesh Ray
Keyword(s):  
Boolean Circuits ◽  
Dna Computer

scholarly journals Simulating Boolean Circuits on a DNA Computer

Algorithmica ◽  
1999 ◽  
Vol 25 (2-3) ◽  
pp. 239-250 ◽  
Author(s):  
M. Ogihara ◽  
A. Ray
Keyword(s):  
Boolean Circuits ◽  
Dna Computer

Chips with Everything

2017 ◽  
Author(s):  
David Segal
Keyword(s):  
Quantum Computing ◽  
Integrated Circuits ◽  
Critical Role ◽  
Moore’S Law ◽  
Moore's Law ◽  
Silicon Chips ◽  
History Of ◽  
Future Potential ◽  
Digital Computers ◽  
Dna Computer

Chapter 3 highlights the critical role materials have in the development of digital computers. It traces developments from the cat’s whisker to valves through to relays and transistors. Accounts are given for transistors and the manufacture of integrated circuits (silicon chips) by use of photolithography. Future potential computing techniques, namely quantum computing and the DNA computer, are covered. The history of computability and Moore’s Law are discussed.

A DNA computer model for solving vertex coloring problem

2006 ◽  
Vol 51 (20) ◽  
pp. 2541-2549 ◽  
Author(s):  
Jin Xu ◽  
Xiaoli Qiang ◽  
Fang Gang ◽  
Kang Zhou
Keyword(s):  
Computer Model ◽  
Vertex Coloring ◽  
Coloring Problem ◽  
Vertex Coloring Problem ◽  
Dna Computer

scholarly journals Additive-error fine-grained quantum supremacy

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 329
Author(s):  
Tomoyuki Morimae ◽  
Suguru Tamaki
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Boolean Circuits ◽  
Exponential Time ◽  
Fine Grained ◽  
Additive Error ◽  
Universal Quantum ◽  
The One ◽  
Computing Models

It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain conjectures in classical complexity theory. Recently, these results have been improved to ``fine-grained" versions where even exponential-time classical simulations are excluded assuming certain classical fine-grained complexity conjectures. All these fine-grained results are, however, about the hardness of strong simulations or multiplicative-error sampling. It was open whether any fine-grained quantum supremacy result can be shown for a more realistic setup, namely, additive-error sampling. In this paper, we show the additive-error fine-grained quantum supremacy (under certain complexity assumptions). As examples, we consider the IQP model, a mixture of the IQP model and log-depth Boolean circuits, and Clifford+T circuits. Similar results should hold for other sub-universal models.

scholarly journals The Computational Complexity of Understanding Binary Classifier Decisions

2021 ◽  
Vol 70 ◽  
Author(s):  
Stephan Waeldchen ◽  
Jan Macdonald ◽  
Sascha Hauch ◽  
Gitta Kutyniok
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Boolean Circuits ◽  
Binary Classifier ◽  
Minimal Set ◽  
Limited Size ◽  
Approximation Factor ◽  
Special Cases ◽  
Relevant Variables ◽  
Binary Classifiers

For a d-ary Boolean function Φ: {0, 1}d → {0, 1} and an assignment to its variables x = (x1, x2, . . . , xd) we consider the problem of finding those subsets of the variables that are sufficient to determine the function value with a given probability δ. This is motivated by the task of interpreting predictions of binary classifiers described as Boolean circuits, which can be seen as special cases of neural networks. We show that the problem of deciding whether such subsets of relevant variables of limited size k ≤ d exist is complete for the complexity class NPPP and thus, generally, unfeasible to solve. We then introduce a variant, in which it suffices to check whether a subset determines the function value with probability at least δ or at most δ − γ for 0 < γ < δ. This promise of a probability gap reduces the complexity to the class NPBPP. Finally, we show that finding the minimal set of relevant variables cannot be reasonably approximated, i.e. with an approximation factor d1−α for α > 0, by a polynomial time algorithm unless P = NP. This holds even with the promise of a probability gap.

Minimal reversible circuit synthesis on a DNA computer

2016 ◽  
Vol 16 (3) ◽  
pp. 463-472 ◽  
Author(s):  
Mayukh Sarkar ◽  
Prasun Ghosal ◽  
Saraju P. Mohanty
Keyword(s):  
Circuit Synthesis ◽  
Reversible Circuit ◽  
Dna Computer
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