Synthesis and Optimization of Reversible Circuits - A Survey

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, transformation-based, 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.Comment: 34 pages, 15 figures, 2 table

Sparsity-Sensitive Finite Abstraction

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network

A Study of Optimal 4-bit Reversible Toffoli Circuits and Their Synthesis

Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results in a huge search space (16! {\approx} 2^{44} functions). The output of such a search alone, counting only the space required to list Toffoli gates for every function, would require over 100 terabytes of storage. In this paper, we present two algorithms: one, that synthesizes an optimal circuit for any 4-bit reversible specification, and another that synthesizes all optimal implementations. We employ several techniques to make the problem tractable. We report results from several experiments, including synthesis of all optimal 4-bit permutations, synthesis of random 4-bit permutations, optimal synthesis of all 4-bit linear reversible circuits, synthesis of existing benchmark functions; we compose a list of the hardest permutations to synthesize, and show distribution of optimal circuits. We further illustrate that our proposed approach may be extended to accommodate physical constraints via reporting LNN-optimal reversible circuits. Our results have important implications in the design and optimization of reversible and quantum circuits, testing circuit synthesis heuristics, and performing experiments in the area of quantum information processing.Comment: arXiv admin note: substantial text overlap with arXiv:1003.191

Synthesis of Linear Reversible Circuits and EXOR-AND-based Circuits for Incompletely Specified Multi-Output Functions

At this time the synthesis of reversible circuits for quantum computing is an active area of research. In the most restrictive quantum computing models there are no ancilla lines and the quantum cost, or latency, of performing a reversible form of the AND gate, or Toffoli gate, increases exponentially with the number of input variables. In contrast, the quantum cost of performing any combination of reversible EXOR gates, or CNOT gates, on n input variables requires at most O(n2/log2n) gates. It was under these conditions that EXOR-AND-EXOR, or EPOE, synthesis was developed. In this work, the GF(2) logic theory used in EPOE is expanded and the concept of an EXOR-AND product transform is introduced. Because of the generality of this logic theory, it is adapted to EXOR-AND-OR, or SPOE, synthesis. Three heuristic spectral logic synthesis algorithms are introduced, implemented in a program called XAX, and compared with previous work in classical logic circuits of up to 26 inputs. Three linear reversible circuit methods are also introduced and compared with previous work in linear reversible logic circuits of up to 100 inputs

ARM2GC: Succinct Garbled Processor for Secure Computation

We present ARM2GC, a novel secure computation framework based on Yao's Garbled Circuit (GC) protocol and the ARM processor. It allows users to develop privacy-preserving applications using standard high-level programming languages (e.g., C) and compile them using off-the-shelf ARM compilers (e.g., gcc-arm). The main enabler of this framework is the introduction of SkipGate, an algorithm that dynamically omits the communication and encryption cost of the gates whose outputs are independent of the private data. SkipGate greatly enhances the performance of ARM2GC by omitting costs of the gates associated with the instructions of the compiled binary, which is known by both parties involved in the computation. Our evaluation on benchmark functions demonstrates that ARM2GC not only outperforms the current GC frameworks that support high-level languages, it also achieves efficiency comparable to the best prior solutions based on hardware description languages. Moreover, in contrast to previous high-level frameworks with domain-specific languages and customized compilers, ARM2GC relies on standard ARM compiler which is rigorously verified and supports programs written in the standard syntax.Comment: 13 page

Design Automation and Application for Emerging Reconfigurable Nanotechnologies

In the last few decades, two major phenomena have revolutionized the electronic industry – the ever-increasing dependence on electronic circuits and the Complementary Metal Oxide Semiconductor (CMOS) downscaling. These two phenomena have been complementing each other in a way that while electronics, in general, have demanded more computations per functional unit, CMOS downscaling has aptly supported such needs. However, while the computational demand is still rising exponentially, CMOS downscaling is reaching its physical limits. Hence, the need to explore viable emerging nanotechnologies is more imperative than ever. This thesis focuses on streamlining the existing design automation techniques for a class of emerging reconfigurable nanotechnologies. Transistors based on this technology exhibit duality in conduction, i.e. they can be configured dynamically either as a p-type or an n-type device on the application of an external bias. Owing to this dynamic reconfiguration, these transistors are also referred to as Reconfigurable Field-Effect Transistors (RFETs). Exploring and developing new technologies just like CMOS, require tackling two main challenges – first, design automation flow has to be modified to enable tailor- made circuit designs. Second, possible application opportunities should be explored where such technologies can outsmart the existing CMOS technologies. This thesis targets the above two objectives for emerging reconfigurable nanotechnologies by proposing approaches for enabling an Electronic Design Automation (EDA) flow for circuits based on RFETs and exploring hardware security as an application that exploits the transistor-level dynamic reconfiguration offered by this technology. This thesis explains the bottom-up approach adopted to propose a logic synthesis flow by identifying new logic gates and circuit design paradigms that can particularly exploit the dynamic reconfiguration offered by these novel nanotechnologies. This led to the subsequent need of finding natural Boolean logic abstraction for emerging reconfigurable nanotechnologies as it is shown that the existing abstraction of negative unate logic for CMOS technologies is sub-optimal for RFETs-based circuits. In this direction, it has been shown that duality in Boolean logic is a natural abstraction for this technology and can truly represent the duality in conduction offered by individual transistors. Finding this abstraction paved the way for defining suitable primitives and proposing various algorithms for logic synthesis and technology mapping. The following step is to explore compatible physical synthesis flow for emerging reconfigurable nanotechnologies. Using silicon nanowire-based RFETs, .lef and .lib files have been provided which can provide an end-to-end flow to generate .GDSII file for circuits exclusively based on RFETs. Additionally, new approaches have been explored to improve placement and routing for circuits based on reconfigurable nanotechnologies. It has been demonstrated how these approaches led to superior results as compared to the native flow meant for CMOS. Lastly, the unique property of transistor-level reconfiguration offered by RFETs is utilized to implement efficient Intellectual Property (IP) protection schemes against adversarial attacks. The ability to control the conduction of individual transistors can be argued as one of the impactful features of this technology and suitably fits into the paradigm of security measures. Prior security schemes based on CMOS technology often come with large overheads in terms of area, power, and delay. In contrast, RFETs-based hardware security measures such as logic locking, split manufacturing, etc. proposed in this thesis, demonstrate affordable security solutions with low overheads. Overall, this thesis lays a strong foundation for the two main objectives – design automation, and hardware security as an application, to push emerging reconfigurable nanotechnologies for commercial integration. Additionally, contributions done in this thesis are made available under open-source licenses so as to foster new research directions and collaborations.:Abstract List of Figures List of Tables 1 Introduction 1.1 What are emerging reconfigurable nanotechnologies? 1.2 Why does this technology look so promising? 1.3 Electronics Design Automation 1.4 The game of see-saw: key challenges vs benefits for emerging reconfigurable nanotechnologies 1.4.1 Abstracting ambipolarity in logic gate designs 1.4.2 Enabling electronic design automation for RFETs 1.4.3 Enhanced functionality: a suitable fit for hardware security applications 1.5 Research questions 1.6 Entire RFET-centric EDA Flow 1.7 Key Contributions and Thesis Organization 2 Preliminaries 2.1 Reconfigurable Nanotechnology 2.1.1 1D devices 2.1.2 2D devices 2.1.3 Factors favoring circuit-flexibility 2.2 Feasibility aspects of RFET technology 2.3 Logic Synthesis Preliminaries 2.3.1 Circuit Model 2.3.2 Boolean Algebra 2.3.3 Monotone Function and the property of Unateness 2.3.4 Logic Representations 3 Exploring Circuit Design Topologies for RFETs 3.1 Contributions 3.2 Organization 3.3 Related Works 3.4 Exploring design topologies for combinational circuits: functionality-enhanced logic gates 3.4.1 List of Combinational Functionality-Enhanced Logic Gates based on RFETs 3.4.2 Estimation of gate delay using the logical effort theory 3.5 Invariable design of Inverters 3.6 Sequential Circuits 3.6.1 Dual edge-triggered TSPC-based D-flip flop 3.6.2 Exploiting RFET’s ambipolarity for metastability 3.7 Evaluations 3.7.1 Evaluation of combinational logic gates 3.7.2 Novel design of 1-bit ALU 3.7.3 Comparison of the sequential circuit with an equivalent CMOS-based design 3.8 Concluding remarks 4 Standard Cells and Technology Mapping 4.1 Contributions 4.2 Organization 4.3 Related Work 4.4 Standard cells based on RFETs 4.4.1 Interchangeable Pull-Up and Pull-Down Networks 4.4.2 Reconfigurable Truth-Table 4.5 Distilling standard cells 4.6 HOF-based Technology Mapping Flow for RFETs-based circuits 4.6.1 Area adjustments through inverter sharings 4.6.2 Technology Mapping Flow 4.6.3 Realizing Parameters For The Generic Library 4.6.4 Defining RFETs-based Genlib for HOF-based mapping 4.7 Experiments 4.7.1 Experiment 1: Distilling standard-cells from a benchmark suite 4.7.2 Experiment 2A: HOF-based mapping . 4.7.3 Experiment 2B: Using the distilled standard-cells during mapping 4.8 Concluding Remarks 5 Logic Synthesis with XOR-Majority Graphs 5.1 Contributions 5.2 Organization 5.3 Motivation 5.4 Background and Preliminaries 5.4.1 Terminologies 5.4.2 Self-duality in NPN classes 5.4.3 Majority logic synthesis 5.4.4 Earlier work on XMG 5.4.5 Classification of Boolean functions 5.5 Preserving Self-Duality 5.5.1 During logic synthesis 5.5.2 During versatile technology mapping 5.6 Advanced Logic synthesis techniques 5.6.1 XMG resubstitution 5.6.2 Exact XMG rewriting 5.7 Logic representation-agnostic Mapping 5.7.1 Versatile Mapper 5.7.2 Support of supergates 5.8 Creating Self-dual Benchmarks 5.9 Experiments 5.9.1 XMG-based Flow 5.9.2 Experimental Setup 5.9.3 Synthetic self-dual benchmarks 5.9.4 Cryptographic benchmark suite 5.10 Concluding remarks and future research directions 6 Physical synthesis flow and liberty generation 6.1 Contributions 6.2 Organization 6.3 Background and Related Work 6.3.1 Related Works 6.3.2 Motivation 6.4 Silicon Nanowire Reconfigurable Transistors 6.5 Layouts for Logic Gates 6.5.1 Layouts for Static Functional Logic Gates 6.5.2 Layout for Reconfigurable Logic Gate 6.6 Table Model for Silicon Nanowire RFETs 6.7 Exploring Approaches for Physical Synthesis 6.7.1 Using the Standard Place & Route Flow 6.7.2 Open-source Flow 6.7.3 Concept of Driver Cells 6.7.4 Native Approach 6.7.5 Island-based Approach 6.7.6 Utilization Factor 6.7.7 Placement of the Island on the Chip 6.8 Experiments 6.8.1 Preliminary comparison with CMOS technology 6.8.2 Evaluating different physical synthesis approaches 6.9 Results and discussions 6.9.1 Parameters Which Affect The Area 6.9.2 Use of Germanium Nanowires Channels 6.10 Concluding Remarks 7 Polymporphic Primitives for Hardware Security 7.1 Contributions 7.2 Organization 7.3 The Shift To Explore Emerging Technologies For Security 7.4 Background 7.4.1 IP protection schemes 7.4.2 Preliminaries 7.5 Security Promises 7.5.1 RFETs for logic locking (transistor-level locking) 7.5.2 RFETs for split manufacturing 7.6 Security Vulnerabilities 7.6.1 Realization of short-circuit and open-circuit scenarios in an RFET-based inverter 7.6.2 Circuit evaluation on sub-circuits 7.6.3 Reliability concerns: A consequence of short-circuit scenario 7.6.4 Implication of the proposed security vulnerability 7.7 Analytical Evaluation 7.7.1 Investigating the security promises 7.7.2 Investigating the security vulnerabilities 7.8 Concluding remarks and future research directions 8 Conclusion 8.1 Concluding Remarks 8.2 Directions for Future Work Appendices A Distilling standard-cells B RFETs-based Genlib C Layout Extraction File (.lef) for Silicon Nanowire-based RFET D Liberty (.lib) file for Silicon Nanowire-based RFET

The EPFL Logic Synthesis Libraries

We present a collection of modular open source C++ libraries for the development of logic synthesis applications. These libraries can be used to develop applications for the design of classical and emerging technologies, as well as for the implementation of quantum compilers. All libraries are well documented and well tested. Furthermore, being header-only, the libraries can be readily used as core components in complex logic synthesis systems.Comment: 11 pages, originally accepted at Int'l Workshop on Logic & Synthesis 2018, extended for Workshop on Open-Source EDA Technology 201