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Reversible Circuit Synthesis of Symmetric Functions Using a Simple Regular Structure
[chapter]
2013
Lecture Notes in Computer Science
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However, the number of garbage outputs increases slightly. To overcome this, we next propose an optimized design by reusing the garbage outputs. ...
The resulting design thus offers a powerful approach towards reversible synthesis of symmetric Boolean functions. ...
If the set A contains only consecutive integers (a l , a l+1 , · · · , a q ) with a l <a q , the symmetric function is called consecutive symmetric function and denoted by S n a l −aq . ...
doi:10.1007/978-3-642-38986-3_15
fatcat:uzj3zjijdreevlubiztswhy474
Cayley graphs and analysis of quantum cost for reversible circuit synthesis
[article]
2012
arXiv
pre-print
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We propose a synthesis algorithm based on the Cayley graph H_n with upper bound of (n-1)2^n+1 multiple-control Toffoli gates. ...
Those two Cayley graphs have degree n2^n-1 and order 2^n!. Maslov, Dueck and Miller proposed a reversible circuit synthesis that we model by the Cayley graph I_n. ...
ACKNOWLEDGEMENTS The authors thank Luís Cunha and Roberto Sampaio for helpful discussions. ...
arXiv:1209.3275v1
fatcat:teej2elejbghtdabdfjkgykdiq
Clean Translation of an Imperative Reversible Programming Language
[chapter]
2011
Lecture Notes in Computer Science
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In particular, target programs only require a constant amount of temporary garbage space. ...
The given translation methods are generic, and should be applicable to any (imperative) reversible source language described with reversible flowcharts and reversible updates. ...
A preliminary version of this work was presented at the 2nd Workshop on Reversible Computing in Bremen, July 2010. ...
doi:10.1007/978-3-642-19861-8_9
fatcat:k3xzwvq3jzd5zfg2od2jntblyu
Quantum Circuit Design of Toom 3-Way Multiplication
2021
Applied Sciences
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Moreover, to further minimize the cost of the remaining division, we utilize the unique property of the particular division circuit, replacing it with a constant multiplication by reciprocal circuit and ...
In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba multiplication ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/app11093752
fatcat:32glnrbbovcrjn3nohkmb6kiri
Quantum circuits for Toom-Cook multiplication
2018
Physical Review A
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2018 pre-print arXiv:1805.02342v1 fatcat:mvvnw5sno5gsxm7q7f25zm6cuyOther Versions
In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. ...
By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. ...
TOOM-COOK MULTIPLIER Given two large integers n 1 and n 2 , the Toom-Cook algorithm splits them into k smaller parts of length l. ...
doi:10.1103/physreva.98.012311
fatcat:6nd6ki33wndwfdbbjd6e6rjgwy
Energy-Efficient Algorithms
2016
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
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On top of these models, we build familiar high-level primitives such as control logic, memory allocation, and garbage collection with zero energy complexity and only constant-factor overheads in space ...
These results lay a theoretical foundation for a new field of semi-reversible computing and provide a new framework for the investigation of algorithms. ...
Acknowledgments We thank Martin Demaine and Kevin Kelley for helpful early discussions about this project, in particular early formulations of the models of computation. We also thank Maria L. ...
doi:10.1145/2840728.2840756
dblp:conf/innovations/DemaineLMT16
fatcat:i6r45uh5cfflje2d7hye2f7ic4
Complexity Analysis of Reversible Logic Synthesis
[article]
2014
arXiv
pre-print
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In this paper, we study the complexity of reversible logic synthesis. The problem is separately studied for bounded-ancilla and ancilla-free optimal synthesis approaches. ...
Finally, experiments are performed with a shortest-path based reversible logic synthesis approach and a (0-1) ILP-based formulation. ...
Conclusion and Future Work In this paper, we studied the complexity of exact reversible logic synthesis, for both the cases of the circuit being bounded-ancilla and ancilla-free. ...
arXiv:1402.0491v3
fatcat:43y7ticgzrdszbconytxyv53kq
Energy-Efficient Algorithms
[article]
2016
arXiv
pre-print
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On top of these models, we build familiar high-level primitives such as control logic, memory allocation, and garbage collection with zero energy complexity and only constant-factor overheads in space ...
These results lay a theoretical foundation for a new field of semi-reversible computing and provide a new framework for the investigation of algorithms. ...
Acknowledgments We thank Martin Demaine and Kevin Kelley for helpful early discussions about this project, in particular early formulations of the models of computation. We also thank Maria L. ...
arXiv:1605.08448v1
fatcat:or7pwl5hlvac7cgwl3uq4faltu
Fault Tolerant Synthesis of Reversible Circuits
[article]
2015
arXiv
pre-print
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2013 pre-print arXiv:1310.5231v1 fatcat:duodp7h4ercqpcl7hdp2eiyua4
In order to extend online testability of reversible circuits, the substitution of Peres gate has been presented. ...
The online testing capabilities of MCF including Swap and Fredkin gates were also identifies. ...
An n+1 bit extended Toffoli gate maps input vectors (k 1 ,k 2 ….k n+1 ) to output vectors (O 1 ,O 2 …O n+1 ) where, O j = k j (for all j < n), On = k 1 k 2 …k n-1 ⊕k n and O n+1 = k 1 k 2 …k n-1 ⊕k n+1 ...
arXiv:1310.5231v2
fatcat:b7fv6qwwybdm3pdwukvvvqumvi
Design and Implementation of Dynamic Memory Management in a Reversible Object-Oriented Programming Language
[article]
2018
arXiv
pre-print
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Translations of the extensions added in ROOPL++ to the reversible assembly language PISA are presented to provide garbage-free computations. ...
Considerations for reversible memory manager layouts are discussed and ultimately lead to the selection of the Buddy Memory layout. ...
A quadruple is either a symbol rule of the form (q 1 , s 1 , s 2 , q 2 ) or a shift rule of the form (q 1 , /, d, q 2 ) where q 1 ∈ Q, q 2 ∈ Q, s 1 ∈ Γ, s 2 ∈ Γ and d being either L or R. ...
arXiv:1804.05097v1
fatcat:rl2idwvlqrg7zcmmpzyuwzq24u
Dynamic memory allocation in computer simulation
1977
Communications of the ACM
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Algorithms maintaining separate free space lists for each size of memory block used tended to perform quite well compared with other algorithms. ...
Algorithms employing LIFO, FIFO, or memory ordered free lists generally performed poorly compared with others. ...
This review resulted in the selection of seven algorithms: 1-2, 1-5, II-2, 11-6, IV-l, V-l, and V-5. ...
doi:10.1145/359863.359890
fatcat:a5iw2pia6nbwxdh26j77ntf7wq
List processing in real time on a serial computer
1978
Communications of the ACM
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allocation is critical, nor compatible, in the sense that a ýystem with both forms of garbage collection is worse than our pure one. ...
T(CONS) is bounded by a constant independent of the number of cells in use; 2) requires space (2+21p)N, i.e. not more than twice that of a classical system; 3) runs on a serial computer without a time-sharing ...
Maximum MKSMW Storage Required < N(1.5+2m) Maximum SRT Storage Required -N(2+2m) If
The Parameter m (= 1/k) If k is a positive integer, then the parameter m (=1/k) will lie in the interval 0<mnil. ...
doi:10.1145/359460.359470
fatcat:e6y6vhb6nvem3fe6hekkz5aisq
An Automata-Theoretic Algorithm for Counting Solutions to Presburger Formulas
[chapter]
2004
Lecture Notes in Computer Science
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We present an algorithm for counting the number of integer solutions to selected free variables of a Presburger formula. ...
We represent the Presburger formula as a deterministic finite automaton (DFA) whose accepting paths encode the standard binary representations of satisfying free variable values. ...
Consider Presburger formula P(i, j, k; n) = 1 ≤ i ≤ n ∧ 3 ≤ j ≤ i ∧ j ≤ k ≤ 5 with free integer variables i, j, and k and symbolic constant n, 1 and consider the sum S(n) = n i=1 i j=3 5 k=j 1 with symbolic ...
doi:10.1007/978-3-540-24723-4_8
fatcat:n4hfzaxfrffpljiywsadka62ba
Higher-Order Separation Logic in Isabelle/HOLCF
2008
Electronical Notes in Theoretical Computer Science
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We use our formalization to give a formally verified proof of Cheney's copying garbage collector [4] using a tagged representation of objects. The proof generalizes the results in [2] . ...
The proof uses an encoding of the separation logic formula this(h) to capture the heap from before the garbage collection and thus shows another novel use of higher-order separation logic. ...
Acknowledgements We thank John Reynolds for interesting discussions regarding our system, and the anonymous referees for their helpful comments. ...
doi:10.1016/j.entcs.2008.10.022
fatcat:dxrjw4q46nfmvk2k6rkgq7z7pi
Shor's discrete logarithm quantum algorithm for elliptic curves
[article]
2004
arXiv
pre-print
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As the runtime of Euclid's algorithm depends on the input, one difficulty encountered is the "quantum halting problem". ...
The main technical difficulty is to implement Euclid's gcd algorithm to compute multiplicative inverses modulo p. ...
An elliptic curve over K is the set of solutions (x, y) ∈ K × K to the equation E : y 2 = x 3 + ax + b (1) where a, b ∈ K are constants such that 4a 3 + 27b 2 = 0, together with the point at infinity, ...
arXiv:quant-ph/0301141v2
fatcat:q5tvmeguarhy3mgaolvqi722li
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