A Sound and Complete Axiomatization of Majority-n Logic

Manipulating logic functions via majority operators recently drew the attention of researchers in computer science. For example, circuit optimization based on majority operators enables superior results as compared to traditional logic systems. Also, the Boolean satisfiability problem finds new solving approaches when described in terms of majority decisions. To support computer logic applications based on majority a sound and complete set of axioms is required. Most of the recent advances in majority logic deal only with ternary majority (MAJ- 3) operators because the axiomatization with solely MAJ-3 and complementation operators is well understood. However, it is of interest extending such axiomatization to n-ary majority operators (MAJ-n) from both the theoretical and practical perspective. In this work, we address this issue by introducing a sound and complete axiomatization of MAJ-n logic. Our axiomatization naturally includes existing majority logic systems. Based on this general set of axioms, computer applications can now fully exploit the expressive power of majority logic.Comment: Accepted by the IEEE Transactions on Computer

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

Asynchronous nanowire crossbar architecture for manufacturability, modularity and robustness

This thesis spotlights the dawn of a promising new nanowire crossbar architecture, the Asynchronous crossbar architecture, in the form of three different articles. It combines the reduced size of the nanowire crossbar architecture with the clock-free nature of Null Conventional Logic, which are the primary advantages. The first paper explains the proposed architecture with illustrations, including the design of an optimized full adder. This architecture has an elementary structure termed as a Programmable Gate Macro Block (PGMB) which is analogous to a threshold gate in NCL. The other two papers concentrate on mapping and placement techniques which are important due to defects involved in crossbars. These defects have to be tolerated and logic has to be routed appropriately for successful functioning of the circuit --Introduction, page 1

On The Design Of Low-Complexity High-Speed Arithmetic Circuits In Quantum-Dot Cellular Automata Nanotechnology

For the last four decades, the implementation of very large-scale integrated systems has largely based on complementary metal-oxide semiconductor (CMOS) technology. However, this technology has reached its physical limitations. Emerging nanoscale technologies such as quantum-dot cellular automata (QCA), single electron tunneling (SET), and tunneling phase logic (TPL) are major candidate for possible replacements of CMOS. These nanotechnologies use majority and/or minority logic and inverters as circuit primitives. In this dissertation, a comprehensive methodology for majority/minority logic networks synthesis is developed. This method is capable of processing any arbitrary multi-output Boolean function to nd its equivalent optimal majority logic network targeting to optimize either the number of gates or levels. The proposed method results in different primary equivalent majority expression networks. However, the most optimized network will be generated as a nal solution. The obtained results for 15 MCNC benchmark circuits show that when the number of majority gates is the rst optimization priority, there is an average reduction of 45.3% in the number of gates and 15.1% in the number of levels. They also show that when the rst priority is the number of levels, an average reduction of 23.5% in the number of levels and 43.1% in the number of gates is possible, compared to the majority AND/OR mapping method. These results are better compared to those obtained from the best existing methods. In this dissertation, our approach is to exploit QCA technology because of its capability to implement high-density, very high-speed switching and tremendously lowpower integrated systems and is more amenable to digital circuits design. In particular, we have developed algorithms for the QCA designs of various single- and multi-operation arithmetic arrays. Even though, majority/minority logic are the basic units in promising nanotechnologies, an XOR function can be constructed in QCA as a single device. The basic cells of the proposed arrays are developed based on the fundamental logic devices in QCA and a single-layer structure of the three-input XOR function. This process leads to QCA arithmetic circuits with better results in view of dierent aspects such as cell count, area, and latency, compared to their best counterparts. The proposed arrays can be formed in a pipeline manner to perform the arithmetic operations for any number of bits which could be quite valuable while considering the future design of large-scale QCA circuits

Probabilistic analysis of defect tolerance in asynchronous nano crossbar architecture

Among recent advancements in technology, nanotechnology is particularly promising. Most researchers have begun to focus their efforts on developing nano scale circuits. Nano scale devices such as carbon nano tubes (CNT) and silicon nano wires (SiNW) form the primitive building blocks of many nano scale logic devices and recently developed computing architecture. One of the most promising nanotechnologies is crossbar-based architecture, a two-dimensional nanoarray, formed by the intersection of two orthogonal sets of parallel and uniformly-spaced CNTs or SiNWs. Nanowire crossbars offer the potential for ultra-high density, which has never been achieved by photolithography. In an effort to improve these circuits, our research group proposed a new Null Convention Logic (NCL) based clock-less crossbar architecture. By eliminating the clock, this architecture makes possible a still higher density in reconfigurable systems. Defect density, however, is directly proportional to the density of nanowires in the architecture. Future work, therefore, must improve the defect tolerance of these asynchronous structures. The thesis comprises two papers. The first introduces asynchronous crossbar architecture and concludes with the validation of mapping a 1-bit adder on it. It also discusses various advantages of asynchronous crossbar architecture over clock based nano structures. The second paper concentrates on the probabilistic analysis of asynchronous nano crossbar architecture to address the high defect rates in these structures. It analyzes the probability distribution of mapping functions over the structure for varying number of defects and proposes a method to increase the probability of successful mapping --Abstract, page iv