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Reversible Circuit Synthesis of Symmetric Functions Using a Simple Regular Structure [chapter]

Arighna Deb, Debesh K. Das, Hafizur Rahaman, Bhargab B. Bhattacharya, Robert Wille, Rolf Drechsler
2013 Lecture Notes in Computer Science  
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]

A. C. Ribeiro, C. M. H. de Figueiredo, F. L. Marquezino, L. A. B. Kowada
2012 arXiv   pre-print
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]

Holger Bock Axelsen
2011 Lecture Notes in Computer Science  
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

Harashta Tatimma Larasati, Asep Muhamad Awaludin, Janghyun Ji, Howon Kim
2021 Applied Sciences  
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

Srijit Dutta, Debjyoti Bhattacharjee, Anupam Chattopadhyay
2018 Physical Review A  
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

Erik D. Demaine, Jayson Lynch, Geronimo J. Mirano, Nirvan Tyagi
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
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]

Anupam Chattopadhyay, Chander Chandak, Kaushik Chakraborty
2014 arXiv   pre-print
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]

Erik D. Demaine, Jayson Lynch, Geronimo J. Mirano, Nirvan Tyagi
2016 arXiv   pre-print
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]

Anugrah Jain
2015 arXiv   pre-print
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 2k n-1k n and O n+1 = k 1 k 2k n-1k n+1  ... 
arXiv:1310.5231v2 fatcat:b7fv6qwwybdm3pdwukvvvqumvi

Design and Implementation of Dynamic Memory Management in a Reversible Object-Oriented Programming Language [article]

Martin Holm Cservenka
2018 arXiv   pre-print
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

Norman R. Nielsen
1977 Communications of the ACM  
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

Henry G. Baker
1978 Communications of the ACM  
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]

Erin Parker, Siddhartha Chatterjee
2004 Lecture Notes in Computer Science  
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

Carsten Varming, Lars Birkedal
2008 Electronical Notes in Theoretical Computer Science  
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]

John Proos, Christof Zalka
2004 arXiv   pre-print
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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