Exploiting Circuit Duality to Speed Up SAT

In this paper, we establish a non-trivial duality between tautology and contradiction check to speed up circuit SAT. Tautology check determines if a logic circuit is true in every possible interpretation. Analogously, contradiction check determines if a logic circuit is false in every possible interpretation. A trivial transformation of a (tautology, contradiction) check problem into a (contradiction, tautology) check problem is the inversion of all outputs in a logic circuit. In this work, we show that exact logic inversion is not necessary. We give operator switching rules that selectively exchange tautologies with contradictions, and vice versa. Our approach collapses into logic inversion just for tautology and contradiction extreme points but generates non-complementary logic circuits in the other cases. This property enables computing benefits when an alternative, but equisolvable, instance of a problem is easier to solve than the original one. As a case study, we investigate the impact on SAT. There, our methodology generates a dual SAT instance solvable in parallel with the original one. This concept can be used on top of any other SAT approach and does not impose much overhead, except having to run two solvers instead of one, which is typically not a problem because multi-cores are widespread and computing resources are inexpensive. Experimental results show a 25% speed-up of SAT in a concurrent execution scenario. Also, statistical experiments confirmed that our runtime reduction is not of the random variation type

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

In various areas of computer science, we deal with a set of constraints to be satisfied. If the constraints cannot be satisfied simultaneously, it is desirable to identify the core problems among them. Such cores are called minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more information about the conflicts among the constraints is obtained. However, a full enumeration of all MUSes is in general intractable due to the large number (even exponential) of possible conflicts. Moreover, to identify MUSes algorithms must test sets of constraints for their simultaneous satisfiabilty. The type of the test depends on the application domains. The complexity of tests can be extremely high especially for domains like temporal logics, model checking, or SMT. In this paper, we propose a recursive algorithm that identifies MUSes in an online manner (i.e., one by one) and can be terminated at any time. The key feature of our algorithm is that it minimizes the number of satisfiability tests and thus speeds up the computation. The algorithm is applicable to an arbitrary constraint domain and its effectiveness demonstrates itself especially in domains with expensive satisfiability checks. We benchmark our algorithm against state of the art algorithm on Boolean and SMT constraint domains and demonstrate that our algorithm really requires less satisfiability tests and consequently finds more MUSes in given time limits

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

Recent Advances in Computational Methods for the Power Flow Equations

The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and voltages in a power system. A plethora of methods have been devised to solve these equations, starting from Newton-based methods to homotopy continuation and other optimization-based methods. While many of these methods often efficiently find a high-voltage, stable solution due to its large basin of attraction, most of the methods struggle to find low-voltage solutions which play significant role in certain stability-related computations. While we do not claim to have exhausted the existing literature on all related methods, this tutorial paper introduces some of the recent advances in methods for solving power flow equations to the wider power systems community as well as bringing attention from the computational mathematics and optimization communities to the power systems problems. After briefly reviewing some of the traditional computational methods used to solve the power flow equations, we focus on three emerging methods: the numerical polynomial homotopy continuation method, Groebner basis techniques, and moment/sum-of-squares relaxations using semidefinite programming. In passing, we also emphasize the importance of an upper bound on the number of solutions of the power flow equations and review the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016 American Control Conferenc

New Data Structures and Algorithms for Logic Synthesis and Verification

The strong interaction between Electronic Design Automation (EDA) tools and Complementary Metal-Oxide Semiconductor (CMOS) technology contributed substantially to the advancement of modern digital electronics. The continuous downscaling of CMOS Field Effect Transistor (FET) dimensions enabled the semiconductor industry to fabricate digital systems with higher circuit density at reduced costs. To keep pace with technology, EDA tools are challenged to handle both digital designs with growing functionality and device models of increasing complexity. Nevertheless, whereas the downscaling of CMOS technology is requiring more complex physical design models, the logic abstraction of a transistor as a switch has not changed even with the introduction of 3D FinFET technology. As a consequence, modern EDA tools are fine tuned for CMOS technology and the underlying design methodologies are based on CMOS logic primitives, i.e., negative unate logic functions. While it is clear that CMOS logic primitives will be the ultimate building blocks for digital systems in the next ten years, no evidence is provided that CMOS logic primitives are also the optimal basis for EDA software. In EDA, the efficiency of methods and tools is measured by different metrics such as (i) the result quality, for example the performance of a digital circuit, (ii) the runtime and (iii) the memory footprint on the host computer. With the aim to optimize these metrics, the accordance to a specific logic model is no longer important. Indeed, the key to the success of an EDA technique is the expressive power of the logic primitives handling and solving the problem, which determines the capability to reach better metrics. In this thesis, we investigate new logic primitives for electronic design automation tools. We improve the efficiency of logic representation, manipulation and optimization tasks by taking advantage of majority and biconditional logic primitives. We develop synthesis tools exploiting the majority and biconditional expressiveness. Our tools show strong results as compared to state-of-the-art academic and commercial synthesis tools. Indeed, we produce the best results for several public benchmarks. On top of the enhanced synthesis power, our methods are the natural and native logic abstraction for circuit design in emerging nanotechnologies, where majority and biconditional logic are the primitive gates for physical implementation. We accelerate formal methods by (i) studying properties of logic circuits and (ii) developing new frameworks for logic reasoning engines. We prove non-trivial dualities for the property checking problem in logic circuits. Our findings enable sensible speed-ups in solving circuit satisfiability. We develop an alternative Boolean satisfiability framework based on majority functions. We prove that the general problem is still intractable but we show practical restrictions that can be solved efficiently. Finally, we focus on reversible logic where we propose a new equivalence checking approach. We exploit the invertibility of computation and the functionality of reversible gates in the formulation of the problem. This enables one order of magnitude speed up, as compared to the state-of-the-art solution. We argue that new approaches to solve EDA problems are necessary, as we have reached a point of technology where keeping pace with design goals is tougher than ever

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

Efficiently Explaining CSPs with Unsatisfiable Subset Optimization (extended algorithms and examples)

We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified using a cost function. The algorithms for explanation generation rely on extracting Minimal Unsatisfiable Subsets (MUS) of a derived unsatisfiable formula, exploiting a one-to-one correspondence between so-called non-redundant explanations and MUSs. However, MUS extraction algorithms do not provide any guarantee of subset minimality or optimality with respect to a given cost function. Therefore, we build on these formal foundations and tackle the main points of improvement, namely how to generate explanations efficiently that are provably optimal (with respect to the given cost metric). For that, we developed (1) a hitting set-based algorithm for finding the optimal constrained unsatisfiable subsets; (2) a method for re-using relevant information over multiple algorithm calls; and (3) methods exploiting domain-specific information to speed up the explanation sequence generation. We experimentally validated our algorithms on a large number of CSP problems. We found that our algorithms outperform the MUS approach in terms of explanation quality and computational time (on average up to 56 % faster than a standard MUS approach).Comment: arXiv admin note: text overlap with arXiv:2105.1176