A Minimum Cut Based Re-synthesis Approach

A new re-synthesis approach that benefits from min-cut based partitioning is proposed. This divide and conquer approach is shown to improve the performance of existing synthesis tools on a variety of benchmarks

Formal Analysis of Arithmetic Circuits using Computer Algebra - Verification, Abstraction and Reverse Engineering

Despite a considerable progress in verification and abstraction of random and control logic, advances in formal verification of arithmetic designs have been lagging. This can be attributed mostly to the difficulty in an efficient modeling of arithmetic circuits and datapaths without resorting to computationally expensive Boolean methods, such as Binary Decision Diagrams (BDDs) and Boolean Satisfiability (SAT), that require “bit blasting”, i.e., flattening the design to a bit-level netlist. Approaches that rely on computer algebra and Satisfiability Modulo Theories (SMT) methods are either too abstract to handle the bit-level nature of arithmetic designs or require solving computationally expensive decision or satisfiability problems. The work proposed in this thesis aims at overcoming the limitations of analyzing arithmetic circuits, specifically at the post-synthesized phase. It addresses the verification, abstraction and reverse engineering problems of arithmetic circuits at an algebraic level, treating an arithmetic circuit and its specification as a properly constructed algebraic system. The proposed technique solves these problems by function extraction, i.e., by deriving arithmetic function computed by the circuit from its low-level circuit implementation using computer algebraic rewriting technique. The proposed techniques work on large integer arithmetic circuits and finite field arithmetic circuits, up to 512-bit wide containing millions of logic gates

Function Verification of Combinational Arithmetic Circuits

Hardware design verification is the most challenging part in overall hardware design process. It is because design size and complexity are growing very fast while the requirement for performance is ever higher. Conventional simulation-based verification method cannot keep up with the rapid increase in the design size, since it is impossible to exhaustively test all input vectors of a complex design. An important part of hardware verification is combinational arithmetic circuit verification. It draws a lot of attention because flattening the design into bit-level, known as the bit-blasting problem, hinders the efficiency of many current formal techniques. The goal of this thesis is to introduce a robust and efficient formal verification method for combinational integer arithmetic circuit based on an in-depth analysis of recent advances in computer algebra. The method proposed here solves the verification problem at bit level, while avoiding bit-blasting problem. It also avoids the expensive Groebner basis computation, typically employed by symbolic computer algebra methods. The proposed method verifies the gate-level implementation of the design by representing the design components (logic gates and arithmetic modules) by polynomials in Z2n . It then transforms the polynomial representing the output bits (called “output signature”) into a unique polynomial in input signals (called “input signature”) using gate-level information of the design. The computed input signature is then compared with the reference input signature (golden model) to determine whether the circuit behaves as anticipated. If the reference input signature is not given, our method can be used to compute (or extract) the arithmetic function of the design by computing its input signature. Additional tools, based on canonical word-level design representations (such as TED or BMD) can be used to determine the function of the computed input signature represents. We demonstrate the applicability of the proposed method to arithmetic circuit verification on a large number of designs

Certifying Correctness for Combinatorial Algorithms : by Using Pseudo-Boolean Reasoning

Over the last decades, dramatic improvements in combinatorialoptimisation algorithms have significantly impacted artificialintelligence, operations research, and other areas. These advances,however, are achieved through highly sophisticated algorithms that aredifficult to verify and prone to implementation errors that can causeincorrect results. A promising approach to detect wrong results is touse certifying algorithms that produce not only the desired output butalso a certificate or proof of correctness of the output. An externaltool can then verify the proof to determine that the given answer isvalid. In the Boolean satisfiability (SAT) community, this concept iswell established in the form of proof logging, which has become thestandard solution for generating trustworthy outputs. The problem isthat there are still some SAT solving techniques for which prooflogging is challenging and not yet used in practice. Additionally,there are many formalisms more expressive than SAT, such as constraintprogramming, various graph problems and maximum satisfiability(MaxSAT), for which efficient proof logging is out of reach forstate-of-the-art techniques.This work develops a new proof system building on the cutting planesproof system and operating on pseudo-Boolean constraints (0-1 linearinequalities). We explain how such machine-verifiable proofs can becreated for various problems, including parity reasoning, symmetry anddominance breaking, constraint programming, subgraph isomorphism andmaximum common subgraph problems, and pseudo-Boolean problems. Weimplement and evaluate the resulting algorithms and a verifier for theproof format, demonstrating that the approach is practical for a widerange of problems. We are optimistic that the proposed proof system issuitable for designing certifying variants of algorithms inpseudo-Boolean optimisation, MaxSAT and beyond

Cryptographic properties of modified AES-like S-boxes

Using AES-like S-boxes (generated using finite field inversion) provides an excellent starting point for generating S-boxes with some specific design criteria dictated by the implemented cipher and still maintaining all the most commonly recognized cryptographic criteria to a large extent. This paper presents the results of statistical analysis of fulfilment of those basic cryptographic criteria by the modified AES-like S-boxes that do have neither equivalence nor cycles

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

SIMD-Swift: Improving Performance of Swift Fault Detection

The general tendency in modern hardware is an increase in fault rates, which is caused by the decreased operation voltages and feature sizes. Previously, the issue of hardware faults was mainly approached only in high-availability enterprise servers and in safety-critical applications, such as transport or aerospace domains. These fields generally have very tight requirements, but also higher budgets. However, as fault rates are increasing, fault tolerance solutions are starting to be also required in applications that have much smaller profit margins. This brings to the front the idea of software-implemented hardware fault tolerance, that is, the ability to detect and tolerate hardware faults using software-based techniques in commodity CPUs, which allows to get resilience almost for free. Current solutions, however, are lacking in performance, even though they show quite good fault tolerance results. This thesis explores the idea of using the Single Instruction Multiple Data (SIMD) technology for executing all program\'s operations on two copies of the same data. This idea is based on the observation that SIMD is ubiquitous in modern CPUs and is usually an underutilized resource. It allows us to detect bit-flips in hardware by a simple comparison of two copies under the assumption that only one copy is affected by a fault. We implemented this idea as a source-to-source compiler which performs hardening of a program on the source code level. The evaluation of our several implementations shows that it is beneficial to use it for applications that are dominated by arithmetic or logical operations, but those that have more control-flow or memory operations are actually performing better with the regular instruction replication. For example, we managed to get only 15% performance overhead on Fast Fourier Transformation benchmark, which is dominated by arithmetic instructions, but memory-access-dominated Dijkstra algorithm has shown a high overhead of 200%

The ghosts of forgotten things: A study on size after forgetting

Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of being a form of reduction, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is $D^p$-hard in $\Sigma^p_2$. The same problem for unrestricted propositional formulae is $D^p_2$-hard in $\Sigma^p_3$. The hardness results employ superredundancy: a superirredundant clause is in all formulae of minimal size equivalent to a given one. This concept may be useful outside forgetting

Efficient alternative wiring techniques and applications.

Sze, Chin Ngai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 80-84) and index.Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiCurriculum Vitae --- p.ivList of Figures --- p.ixList of Tables --- p.xiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation and Aims --- p.1Chapter 1.2 --- Contribution --- p.8Chapter 1.3 --- Organization of Dissertation --- p.10Chapter 2 --- Definitions and Notations --- p.11Chapter 3 --- Literature Review --- p.15Chapter 3.1 --- Logic Reconstruction --- p.15Chapter 3.1.1 --- SIS: A System for Sequential and Combinational Logic Synthesis --- p.16Chapter 3.2 --- ATPG-based Alternative Wiring --- p.17Chapter 3.2.1 --- Redundancy Addition and Removal for Logic Optimization --- p.18Chapter 3.2.2 --- Perturb and Simplify Logic Optimization --- p.18Chapter 3.2.3 --- REWIRE --- p.21Chapter 3.2.4 --- Implication-tree Based Alternative Wiring Logic Trans- formation --- p.22Chapter 3.3 --- Graph-based Alternative Wiring --- p.24Chapter 4 --- Implication Based Alternative Wiring Logic Transformation --- p.25Chapter 4.1 --- Source Node Implication --- p.25Chapter 4.1.1 --- Introduction --- p.25Chapter 4.1.2 --- Implication Relationship and Implication-tree --- p.25Chapter 4.1.3 --- Selection of Alternative Wire Based on Implication-tree --- p.29Chapter 4.1.4 --- Implication-tree Based Logic Transformation --- p.32Chapter 4.2 --- Destination Node Implication --- p.35Chapter 4.2.1 --- Introduction --- p.35Chapter 4.2.2 --- Destination Node Relationship --- p.35Chapter 4.2.3 --- Destination Node Implication-tree --- p.39Chapter 4.2.4 --- Selection of Alternative Wire --- p.41Chapter 4.3 --- The Algorithm --- p.43Chapter 4.3.1 --- IB AW Implementation --- p.43Chapter 4.3.2 --- Experimental Results --- p.43Chapter 4.4 --- Conclusion --- p.45Chapter 5 --- Graph Based Alternative Wiring Logic Transformation --- p.47Chapter 5.1 --- Introduction --- p.47Chapter 5.2 --- Notations and Definitions --- p.48Chapter 5.3 --- Alternative Wire Patterns --- p.50Chapter 5.4 --- Construction of Minimal Patterns --- p.54Chapter 5.4.1 --- Minimality of Patterns --- p.54Chapter 5.4.2 --- Minimal Pattern Formation --- p.56Chapter 5.4.3 --- Pattern Extraction --- p.61Chapter 5.5 --- Experimental Results --- p.63Chapter 5.6 --- Conclusion --- p.63Chapter 6 --- Logic Optimization by GBAW --- p.66Chapter 6.1 --- Introduction --- p.66Chapter 6.2 --- Logic Simplification --- p.67Chapter 6.2.1 --- Single-Addition-Multiple-Removal by Pattern Feature . . --- p.67Chapter 6.2.2 --- Single-Addition-Multiple-Removal by Combination of Pat- terns --- p.68Chapter 6.2.3 --- Single-Addition-Single-Removal --- p.70Chapter 6.3 --- Incremental Perturbation Heuristic --- p.71Chapter 6.4 --- GBAW Optimization Algorithm --- p.73Chapter 6.5 --- Experimental Results --- p.73Chapter 6.6 --- Conclusion --- p.76Chapter 7 --- Conclusion --- p.78Bibliography --- p.80Chapter A --- VLSI Design Cycle --- p.85Chapter B --- Alternative Wire Patterns in [WLFOO] --- p.87Chapter B.1 --- 0-local Pattern --- p.87Chapter B.2 --- 1-local Pattern --- p.88Chapter B.3 --- 2-local Pattern --- p.89Chapter B.4 --- Fanout-reconvergent Pattern --- p.90Chapter C --- New Alternative Wire Patterns --- p.91Chapter C.1 --- Pattern Cluster C1 --- p.91Chapter C.1.1 --- NAND-NAND-AND/NAND;AND/NAND --- p.91Chapter C.1.2 --- NOR-NOR-OR/NOR;AND/NAND --- p.92Chapter C.1.3 --- AND-NOR-OR/NOR;OR/NOR --- p.95Chapter C.1.4 --- OR-NAND-AND/NAND;AND/NAND --- p.95Chapter C.2 --- Pattern Cluster C2 --- p.98Chapter C.3 --- Pattern Cluster C3 --- p.99Chapter C.4 --- Pattern Cluster C4 --- p.104Chapter C.5 --- Pattern Cluster C5 --- p.105Glossary --- p.106Index --- p.10