Logic Synthesis for Established and Emerging Computing

Logic synthesis is an enabling technology to realize integrated computing systems, and it entails solving computationally intractable problems through a plurality of heuristic techniques. A recent push toward further formalization of synthesis problems has shown to be very useful toward both attempting to solve some logic problems exactly--which is computationally possible for instances of limited size today--as well as creating new and more powerful heuristics based on problem decomposition. Moreover, technological advances including nanodevices, optical computing, and quantum and quantum cellular computing require new and specific synthesis flows to assess feasibility and scalability. This review highlights recent progress in logic synthesis and optimization, describing models, data structures, and algorithms, with specific emphasis on both design quality and emerging technologies. Example applications and results of novel techniques to established and emerging technologies are reported

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

Boolean Logic Optimization in Majority-Inverter Graphs

We present a Boolean logic optimization framework based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. Current MIG optimization is supported by a consistent algebraic framework. However, when algebraic methods cannot improve a result quality, stronger Boolean methods are needed to attain further optimization. For this purpose, we propose MIG Boolean methods exploiting the error masking property of majority operators. Our MIG Boolean methods insert logic errors that strongly simplify an MIG while being successively masked by the voting nature of majority nodes. Thanks to the datastructure/ methodology fitness, our MIG Boolean methods run in principle as fast as algebraic counterparts. Experiments show that our Boolean methodology combined with state-of-art MIG algebraic techniques enable superior optimization quality. For example, when targeting depth reduction, our MIG optimizer transforms a ripple carry adder into a carry look-ahead one. Considering the set of IWLS’05 (arithmetic intensive) benchmarks, our MIG optimizer reduces by 17.98% (26.69%) the logic network depth while also enhancing size and power activity metrics, with respect to ABC academic optimizer. Without MIG Boolean methods, i.e., using MIG algebraic optimization alone, the previous gains are halved. Employed as front-end to a delay-critical 22-nm ASIC flow (logic synthesis + physical design) our MIG optimizer reduces the average delay/area/power by (15.07%, 4.93%, 1.93%), over 27 academic and industrial benchmarks, as compared to a leading commercial ASIC flow

A Logical Approach to Real Options Identification with Application to UAV Systems

Complex systems are subject to uncertainties that may lead to suboptimal performance or even catastrophic failure if unmanaged. Uncertainties may be managed through real options that provide a decision maker with the right, but not the obligation, to exercise actions in the future. While real options analysis has traditionally been used to quantify the value of such flexibility, this paper is motivated by the need for a structured approach to identify where real options are or can be embedded for uncertainty management. We introduce a logical model-based approach to identification of real option mechanisms and types, where the mechanism is the enabler of the option, while the type refers to the flexibility provided by the option. First, we extend the classical design structure matrix and the more general multiple-domain matrix (MDM), commonly used in modeling and analyzing interdependencies in complex socio-technical systems, to the more expressive Logical-MDM that supports the representation of flexibility. Second, we show that, in addition to flexibility, two new properties, namely, optionability and realizability, are relevant to the identification of real options. We use the Logical-MDM to estimate flexibility, optionability, and realizability metrics. Finally, we introduce the Real Options Identification (ROI) method based on these metrics, where the identified options are valued using standard real options valuation methods to support decision making under uncertainty. The expressivity of the logic combined with the structure of the dependency model allows the effective representation and identification of mechanisms and types of real options across multiple domains and lifecycle phases of a system. We demonstrate this approach through a series of unmanned air vehicle scenarios

Exploiting Satisfiability Solvers for Efficient Logic Synthesis

Logic synthesis is an important part of electronic design automation (EDA) flows, which enable the implementation of digital systems. As the design size and complexity increase, the data structures and algorithms for logic synthesis must adapt and improve in order to keep pace and to maintain acceptable runtime and high-quality results. Large circuits were often represented using binary decision diagrams (BDDs) that were rapidly adopted by logic synthesis tools beginning in the 1980s. Nowadays, BDD-based algorithms are still enhanced, but the possibilities for improvement are somewhat saturated after some 35 years of research. Alternatively, the first EDA applications that exploit Boolean satisfiability (SAT) were developed in the 1990s. Despite the worst-case exponential runtime of SAT solvers, rapid progress in their performance enabled the creation of efficient SAT-based algorithms. Yet, logic synthesis started using SAT solvers more diffusely only in the last decade. Therefore, thorough research is still required both for exploiting SAT solvers and for encoding logic synthesis problems into SAT. Our main goal in this thesis is to facilitate and promote the further integration of SAT solvers into EDA by proposing and evaluating novel SAT-based algorithms that can be used as building blocks in logic synthesis tools. First, we propose a rapid algorithm for LEXSAT, which generates satisfying assignments in lexicographic order. We show that LEXSAT can bring canonicity, which guarantees the generation of unique results, when using SAT solvers in EDA applications. Next, we present a new SAT-based algorithm that progressively generates irredundant sums of products (SOPs), which still play a crucial role in many logic synthesis tools. Using LEXSAT, for the first time, we can generate canonical SAT-based SOPs that, much like BDD-based SOPs, are unique for a given function and variable order but could relax canonicity in order to improve speed and scalability. Unlike BDDs, due to its progressive nature, our algorithm can generate partial SOPs for applications that can work with incomplete circuit functionality. It is noteworthy that both LEXSAT and the SAT-based SOPs are applicable beyond logic synthesis and EDA. Finally, we focus on resubstitution, which reimplements a given Boolean function as a new function that depends on a set of existing functions called divisors. We propose the carving interpolation algorithm that, unlike the traditional Craig interpolation, forces the use of a specific divisor as an input of the new function. This is particularly useful for global circuit restructuring and for some synthesis-based engineering change order (ECO) algorithms. Furthermore, we compare two existing SAT-based methodologies for resubstitution, which are used for post-mapping logic optimisation. The first methodology combines SAT-based functional dependency checking and Craig interpolation that are also used for our carving interpolation; the second methodology is based on cube enumeration and is similar to the SAT-based SOP generation. The initial implementations of our novel SAT-based algorithms offer either better performance or new features, or both, compared to their state-of-the-art versions. As the results indicate, a further thorough development of SAT-based algorithms for logic synthesis, like the one performed for BDDs in the past, can help overcome existing limitations and keep up with growing designs and design complexity

Multiple sequence alignment correction using constraints

Trabalho apresentado no âmbito do European Master in Computational Logics, como requisito parcial para obtenção do grau de Mestre em Computational LogicsOne of the most important fields in bioinformatics has been the study of protein sequence alignments. The study of homologous proteins, related by evolution, shows the conservation of many amino acids because of their functional and structural importance. One particular relationship between the amino acid sites in the same sequence or between different sequences, is protein-coevolution, interest in which has increased as a consequence of mathematical and computational methods used to understand the spatial, functional and evolutionary dependencies between amino acid sites. The principle of coevolution means that some amino acids are related through evolution because mutations in one site can create evolutionary pressures to select compensatory mutations in other sites that are functionally or structurally related. With the actual methods to detect coevolution, specifically mutual information techniques from the information theory field, we show in this work that much of the information between coevolved sites is lost because of mistakes in the multiple sequence alignment of variable regions. Moreover, we show that using these statistical methods to detect coevolved sites in multiple sequence alignments results in a high rate of false positives. Due to the amount of errors in the detection of coevolved site from multiple sequence alignments, we propose in this work a method to improve the detection efficacy of coevolved sites and we implement an algorithm to fix such sites correcting the misalignment produced in those specific locations. The detection part of our work is based on the mutual information between sites that are guessed as having coevolved, due to their high statistical correlation score. With this information we search for possible misalignments on those regions due to the incorrect matching of amino acids during the alignment. The re-alignment part is based on constraint programming techniques, to avoid the combinatorial complexity when one amino acid can be aligned with many others and to avoid inconsistencies in the alignments. In this work, we present a framework to impose constraints over the sequences, and we show how it is possible to compute alignments based on different criteria just by setting constraint between the amino acids. This framework can be applied not only for improving the alignment and detection of coevolved regions, but also to any desired constraints that may be used to express functional or structural relations among the amino acids in multiple sequences. We show also that after we fix these misalignments, using constraints based techniques, the correlation between coevolved sites increases and, in general, the new alignment is closer to the correct alignment than the MSA alignment. Finally, we show possible future research lines with the objective of overcoming some drawbacks detected during this work