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2017, ArXiv
Synthesis of reversible logic circuits has gained great atten- tion during the last decade. Various synthesis techniques have been pro- posed, some generate optimal solutions (in gate count) and are termed as exact, while others are scalable in the sense that they can handle larger functions but generate sub-optimal solutions. Although scalable synthe- sis is very much essential for circuit design, exact synthesis is also of great importance as it helps in building design library for the synthesis of larger functions. In this paper, we propose an exact synthesis technique for re- versible circuits using model checking. We frame the synthesis problem as a model checking instance and propose an iterative bounded model checking calls for an optimal synthesis. Experiments on reversible logic benchmarks shows successful synthesis of optimal circuits. We also illus- trate optimal synthesis of random functions with as many as 10 variables and up to 10 gates.
2006 IEEE International Conference on Evolutionary Computation, 2006
This paper presents a constructive synthesis algorithm for any n-qubit reversible function. Given any nqubit reversible function, there are N distinct input patterns different from their corresponding outputs, where N ≤ 2 n , and the other (2 n − N) input patterns will be the same as their outputs. We show that this circuit can be synthesized by at most 2n • N '(n − 1)'-CNOT gates and 4n 2 • N NOT gates. The time complexity of our algorithm has asymptotic upper bound O(n • 4 n). The space complexity of our synthesis algorithm is also O(n • 2 n). The computational complexity of our synthesis algorithm is exponentially lower than the complexity of breadthfirst search based synthesis algorithm.
2004
Reversible logic has applications in many fields, including quantum computing. Synthesis techniques for reversible circuits are not well developed, even for functions with a small number of inputs and outputs. This paper proposes an approach to reversible logic synthesis using a new complexity measure based on shared binary decision diagrams with complemented edges (instead of truth tables or PPRM forms, as in the previous algorithms). The approach can be used with arbitrary libraries of reversible logic gates and arbitrary cost functions. Experiments show promising results in comparison with the known approaches.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2006
Reversible logic finds many applications, especially in the area of quantum computing. A completely specified n-input, n-output Boolean function is called reversible if it maps each input assignment to a unique output assignment and vice versa. Logic synthesis for reversible functions differs substantially from traditional logic synthesis and is currently an active area of research. The authors present an algorithm and tool for the synthesis of reversible functions. The algorithm uses the positive-polarity Reed-Muller expansion of a reversible function to synthesize the function as a network of Toffoli gates. At each stage, candidate factors, which represent subexpressions common between the Reed-Muller expansions of multiple outputs, are explored in the order of their attractiveness. The algorithm utilizes a prioritybased search tree, and heuristics are used to rapidly prune the search space. The synthesis algorithm currently targets the generalized n-bit Toffoli gate library. However, other algorithms exist that can convert an n-bit Toffoli gate into a cascade of smaller Toffoli gates. Experimental results indicate that the authors' algorithm quickly synthesizes circuits when tested on the set of all reversible functions of three variables. Furthermore, it is able to quickly synthesize all four-variable and most five-variable reversible functions that were in the test suite. The authors also present results for some benchmark functions widely discussed in literature and some new benchmarks that the authors have developed. The algorithm is shown to synthesize many, but not all, randomly generated reversible functions of as many as 16 variables with a maximum gate count of 25.
Microelectronics Journal, 2010
Synthesis of reversible logic has received significant attention in the recent years and many synthesis approaches for reversible circuits have been proposed so far. In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is introduced to construct a reversible specification from an irreversible function. In addition, a cycle-based representation model is presented to be used as an intermediate format in the proposed synthesis methodology. The selected intermediate format serves as a focal point for all potential representation models.
Design, Automation, and Test in Europe, 2004
A function is reversible if each input vector produces a unique output vector. Reversible functions find applications in low power design, quantum computing, and nanotechnology. Logic synthesis for reversible circuits differs substantially from traditional logic synthesis. In this paper, we present the .rst practical synthesis algorithm and tool for reversible functions with a large number of inputs. It uses positive-polarity
2008 11th EUROMICRO Conference on Digital System Design Architectures, Methods and Tools, 2008
In this paper, a simple and fast algorithm for the synthesis of reversible circuits is presented. This algorithm considers the synthesis process as a kind of sorting problem, generating a reversible circuit composed of CNOT-based gates. We prove that the proposed algorithm converges for any given specification. The empirical results of realizing examples discussed in the literature are reported. The results show that the algorithm leads to a near optimum solution for all 3*3 specifications and very good results for other larger specifications in much fewer steps compared to the search based and other previous algorithms.
2000
Reversible circuits are currently on of top approaches to power minimization and the one whose importance will be only growing with time. In this paper, the well known Feynman gate is generalized to k*k gate and a new generalized k*k family of reversible gates is proposed. A synthesis method for multi-output SOP function using cascades of the new gate family
2004
In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of New Brunswick, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms -search-based, cycle-based, transformationbased, and BDD-based -as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.
ACM Journal on Emerging Technologies in Computing Systems, 2010
Reversible logic has applications in various research areas including signal processing, cryptography and quantum computation. In this paper, direct NCT-based synthesis of a given k-cycle in a cycle-based synthesis scenario is examined. To this end, a set of seven building blocks is proposed that reveals the potential of direct synthesis of a given permutation to reduce both quantum cost and average runtime. To synthesize a given large cycle, we propose a decomposition algorithm to extract the suggested building blocks from the input specification. Then, a synthesis method is introduced which uses the building blocks and the decomposition algorithm. Finally, a hybrid synthesis framework is suggested which uses the proposed cycle-based synthesis method in conjunction with one of the recent NCT-based synthesis approaches which is based on Reed-Muller (RM) spectra. The time complexity and the effectiveness of the proposed synthesis approach are analyzed in detail. Our analyses show that the proposed hybrid framework leads to a better quantum cost in the worst-case scenario compared to the previously presented methods. The proposed framework always converges and typically synthesizes a given specification very fast compared to the available synthesis algorithms. Besides, the quantum costs of benchmark functions are improved about 20% on average (55% in the best case).
Calcolo, 2008
ABSTRACT We present fast algorithms to synthesize exact minimal reversible circuits for various types of gate and cost. By reducing reversible logic synthesis problems to permutation group problems, we use the powerful algebraic software GAP to solve such problems. Our approach can minimize for arbitrary cost functions of gates. In addition, we show that Peres gates are a better choice than the standard Toffoli gates in libraries of universal reversible gates.
International Workshop on Logic …, 2002
A reversible circuit maps each output vector into a unique input vector, and vice versa. CMOS reversible / adiabatic circuits are currently the most important approaches to power optimization. This paper introduces an approach to synthesize generalized multi-rail reversible cascades for singleoutput Boolean functions. Minimizing the "garbage bits" is the main challenge of reversible logic synthesis. Experimental results over a set of single output functions (derived from Espresso PLAs) will be presented at IWLS 2002.
… Conference, 2009. DAC'09. 46th ACM/ …, 2009
Reversible logic is the basis for several emerging technologies such as quantum computing, optical computing, or DNA computing and has further applications in domains like low-power design and nanotechnologies. However, current methods for the synthesis of reversible logic are limited, i.e. they are applicable to relatively small functions only. In this paper, we propose a synthesis approach, that can cope with Boolean functions containing more than a hundred of variables. We present a technique to derive reversible circuits for a function given by a Binary Decision Diagram (BDD). The circuit is obtained using an algorithm with linear worst case behavior regarding run-time and space requirements. Furthermore, the size of the resulting circuit is bounded by the BDD size. This allows to transfer theoretical results known from BDDs to reversible circuits. Experiments show better results (with respect to the circuit cost) and a significantly better scalability in comparison to previous synthesis approaches.
Facta universitatis-series: …, 2010
This paper presents a new algorithm MP (multiple pass) to synthesize large reversible binary circuits without ancilla bits. The well-known MMD algorithm for synthesis of reversible circuits requires to store a truth table (or a Reed-Muller-RM transform) as a 2n vector to ...
As the number of transistors per unit chip area increases, the power dissipation of the chip becomes a bottleneck. New nano-technology materials have been proposed as viable alternatives to CMOS to tackle area and power issues. The power consumption can be minimized by the use of reversible logic instead of conventional combinational circuits. Theoretically, reversible circuits do not consume any power (or consume minimal power) when performing computations. This is achieved by avoiding information loss across the circuit. However, use of reversible circuits to implement digital logic requires development of new Electronic Design Automation techniques. Several approaches have been proposed and each method has its own pros and cons. This often results in multiple designs for the same function. Consequently, this demands research in efficient equivalence checking techniques for reversible circuits.
2009
Synthesis of reversible logic has received significant attention in the recent years and many synthesis approaches for reversible logic have been proposed so far. In this paper, a librarybased synthesis approach for reversible circuits is proposed where an input specification is considered as a permutation comprising a set of cycles. In order to synthesize a given permutation, a library which contains seven building blocks is used where each building block is a cycle of length less than 6. We also propose a decomposition algorithm which produces all possible minimal and inequivalent factorizations for a given cycle of length greater than 5. All decompositions contain the maximum number of disjoint cycles. The generated decompositions are used in conjunction with a cycle assignment algorithm which is proposed based on the graph matching problem to select the best possible cycle pairs. Then, each pair is synthesized by using the available components of the library. The decomposition a...
Arxiv preprint arXiv:0710.0664, 2007
Reversible logic [4, 11] is one of the hot areas of research. It has many applications in quantum computation [13, 23], low-power CMOS [8, 31] and many more. Synthesis and optimization of reversible circuits cannot be done using conventional ways [29]. The design and analysis ...
2007 IEEE/ACM International Conference on Computer-Aided Design, 2007
In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer steps. To evaluate the proposed method, several circuits taken from the literature are used. The experimental results corroborate the expected findings.
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