Boolean Satisfiability in Electronic Design Automation

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks

Test Generation Based on CLP

Functional ATPGs based on simulation are fast, but generally, they are unable to cover corner cases, and they cannot prove untestability. On the contrary, functional ATPGs exploiting formal methods, being exhaustive, cover corner cases, but they tend to suffer of the state explosion problem when adopted for verifying large designs. In this context, we have defined a functional ATPG that relies on the joint use of pseudo-deterministic simulation and Constraint Logic Programming (CLP), to generate high-quality test sequences for solving complex problems. Thus, the advantages of both simulation-based and static-based verification techniques are preserved, while their respective drawbacks are limited. In particular, CLP, a form of constraint programming in which logic programming is extended to include concepts from constraint satisfaction, is well-suited to be jointly used with simulation. In fact, information learned during design exploration by simulation can be effectively exploited for guiding the search of a CLP solver towards DUV areas not covered yet. The test generation procedure relies on constraint logic programming (CLP) techniques in different phases of the test generation procedure. The ATPG framework is composed of three functional ATPG engines working on three different models of the same DUV: the hardware description language (HDL) model of the DUV, a set of concurrent EFSMs extracted from the HDL description, and a set of logic constraints modeling the EFSMs. The EFSM paradigm has been selected since it allows a compact representation of the DUV state space that limits the state explosion problem typical of more traditional FSMs. The first engine is randombased, the second is transition-oriented, while the last is fault-oriented. The test generation is guided by means of transition coverage and fault coverage. In particular, 100% transition coverage is desired as a necessary condition for fault detection, while the bit coverage functional fault model is used to evaluate the effectiveness of the generated test patterns by measuring the related fault coverage. A random engine is first used to explore the DUV state space by performing a simulation-based random walk. This allows us to quickly fire easy-to-traverse (ETT) transitions and, consequently, to quickly cover easy-to-detect (ETD) faults. However, the majority of hard-to-traverse (HTT) transitions remain, generally, uncovered. Thus, a transition-oriented engine is applied to cover the remaining HTT transitions by exploiting a learning/backjumping-based strategy. The ATPG works on a special kind of EFSM, called SSEFSM, whose transitions present the most uniformly distributed probability of being activated and can be effectively integrated to CLP, since it allows the ATPG to invoke the constraint solver when moving between EFSM states. A constraint logic programming-based (CLP) strategy is adopted to deterministically generate test vectors that satisfy the guard of the EFSM transitions selected to be traversed. Given a transition of the SSEFSM, the solver is required to generate opportune values for PIs that enable the SSEFSM to move across such a transition. Moreover, backjumping, also known as nonchronological backtracking, is a special kind of backtracking strategy which rollbacks from an unsuccessful situation directly to the cause of the failure. Thus, the transition-oriented engine deterministically backjumps to the source of failure when a transition, whose guard depends on previously set registers, cannot be traversed. Next it modifies the EFSM configuration to satisfy the condition on registers and successfully comes back to the target state to activate the transition. The transition-oriented engine generally allows us to achieve 100% transition coverage. However, 100% transition coverage does not guarantee to explore all DUV corner cases, thus some hard-to-detect (HTD) faults can escape detection preventing the achievement of 100% fault coverage. Therefore, the CLP-based fault-oriented engine is finally applied to focus on the remaining HTD faults. The CLP solver is used to deterministically search for sequences that propagate the HTD faults observed, but not detected, by the random and the transition-oriented engine. The fault-oriented engine needs a CLP-based representation of the DUV, and some searching functions to generate test sequences. The CLP-based representation is automatically derived from the S2EFSM models according to the defined rules, which follow the syntax of the ECLiPSe CLP solver. This is not a trivial task, since modeling the evolution in time of an EFSM by using logic constraints is really different with respect to model the same behavior by means of a traditional HW description language. At first, the concept of time steps is introduced, required to model the SSEFSM evolution through the time via CLP. Then, this study deals with modeling of logical variables and constraints to represent enabling functions and update functions of the SSEFSM. Formal tools that exhaustively search for a solution frequently run out of resources when the state space to be analyzed is too large. The same happens for the CLP solver, when it is asked to find a propagation sequence on large sequential designs. Therefore we have defined a set of strategies that allow to prune the search space and to manage the complexity problem for the solver

Quality and Quantity in Robustness-Checking Using Formal Techniques

Fault tolerance is one of the main challenges for future technology scaling to tolerate transient faults. Various techniques at design level are available to catch and handle transient faults, e.g., Triple Modular Redundancy. An important but missing step is to verify the implementation of those techniques since the implementation might be buggy itself. The thesis is focusing on formally verifying digital circuits with respect to fault-tolerant aspects. It considers transient faults and basically checks whether these faults can influence the output behavior of sequential circuits for any kind of scenarios. As a result the designer is pin-pointed directly to critical parts of the design and gets a prove about the absence of faulty behavior for non-critical parts. The focus of the verification is completeness with respect to the analysis. Three issues need to be adequately addressed: 1) cover all input stimuli, 2) all possible transient faults, and, 3) all possibly exponential long (wrt. to number of state bits) propagation paths. All three issues are addressed in different engines. A tool called RobuCheck has been implemented and evaluated on different academic benchmarks from ITC'99 and industrial benchmarks from IBM

Design and test for timing uncertainty in VLSI circuits.

由於特徵尺寸不斷縮小，集成電路在生產過程中的工藝偏差在運行環境中溫度和電壓等參數的波動以及在使用過程中的老化等效應越來越嚴重，導致芯片的時序行為出現很大的不確定性。多數情況下，芯片的關鍵路徑會不時出現時序錯誤。加入更多的時序餘量不是一種很好的解決方案，因為這種保守的設計方法會抵消工藝進步帶來的性能上的好處。這就為設計一個時序可靠的系統提出了極大的挑戰，其中的一些關鍵問題包括：(一)如何有效地分配有限的功率預算去優化那些正爆炸式增加的關鍵路徑的時序性能；(二)如何產生能夠捕捉準確的最壞情況時延的高品質測試向量；(三)為了能夠取得更好的功耗和性能上的平衡，我們將不得不允許芯片在使用過程中出現一些頻率很低的時序錯誤。隨之而來的問題是如何做到在線的檢錯和糾錯。為了解決上述問題，我們首先發明了一種新的技術用於識別所謂的虛假路徑，該方法使我們能夠發現比傳統方法更多的虛假路徑。當將所提取的虛假路徑集成到靜態時序分析工具里以後，我們可以得到更為準確的時序分析結果，同時也能節省本來用於優化這些路徑的成本。接著，考慮到現有的延時自動向量生成(ATPG) 方法會產生功能模式下無法出現的測試向量，這種向量可能會造成測試過程中在被激活的路徑周圍出現過多(或過少)的電源噪聲(PSN) ，從而導致測試過度或者測試不足情況。為此，我們提出了一種新的偽功能ATPG工具。通過同時考慮功能約束以及電路的物理佈局信息，我們使用類似ATPG 的算法產生狀態跳變使其能最大化已激活的路徑周圍的PSN影響。最後，基於近似電路的原理，我們提出了一種新的在線原位校正技術，即InTimeFix，用於糾正時序錯誤。由於實現近似電路的綜合僅需要簡單的電路結構分析，因此該技術能夠很容易的擴展到大型電路設計上去。With technology scaling, integrated circuits (ICs) suffer from increasing process, voltage, and temperature (PVT) variations and aging effects. In most cases, these reliability threats manifest themselves as timing errors on speed-paths (i.e., critical or near-critical paths) of the circuit. Embedding a large design guard band to prevent timing errors to occur is not an attractive solution, since this conservative design methodology diminishes the benefit of technology scaling. This creates several challenges on build a reliable systems, and the key problems include (i) how to optimize circuit’s timing performance with limited power budget for explosively increased potential speed-paths; (ii) how to generate high quality delay test pattern to capture ICs’ accurate worst-case delay; (iii) to have better power and performance tradeoff, we have to accept some infrequent timing errors in circuit’s the usage phase. Therefore, the question is how to achieve online timing error resilience.To address the above issues, we first develop a novel technique to identify so-called false paths, which facilitate us to find much more false paths than conventional methods. By integrating our identified false paths into static timing analysis tool, we are able to achieve more accurate timing information and also save the cost used to optimize false paths. Then, due to the fact that existing delay automated test pattern generation (ATPG) methods may generate test patterns that are functionally-unreachable, and such patterns may incur excessive (or limited) power supply noise (PSN) on sensitized paths in test mode, thus leading to over-testing or under-testing of the circuits, we propose a novel pseudo-functional ATPG tool. By taking both circuit layout information and functional constrains into account, we use ATPG like algorithm to justify transitions that pose the maximized functional PSN effects on sensitized critical paths. Finally, we propose a novel in-situ correction technique to mask timing errors, namely InTimeFix, by introducing redundant approximation circuit with more timing slack for speed-paths into the design. The synthesis of the approximation circuit relies on simple structural analysis of the original circuit, which is easily scalable to large IC designs.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Yuan, Feng.Thesis (Ph.D.)--Chinese University of Hong Kong, 2012.Includes bibliographical references (leaves 88-100).Abstract also in Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Challenges to Solve Timing Uncertainty Problem --- p.2Chapter 1.2 --- Contributions and Thesis Outline --- p.5Chapter 2 --- Background --- p.7Chapter 2.1 --- Sources of Timing Uncertainty --- p.7Chapter 2.1.1 --- Process Variation --- p.7Chapter 2.1.2 --- Runtime Environment Fluctuation --- p.9Chapter 2.1.3 --- Aging Effect --- p.10Chapter 2.2 --- Technical Flow to Solve Timing Uncertainty Problem --- p.10Chapter 2.3 --- False Path --- p.12Chapter 2.3.1 --- Path Sensitization Criteria --- p.12Chapter 2.3.2 --- False Path Aware Timing Analysis --- p.13Chapter 2.4 --- Manufacturing Testing --- p.14Chapter 2.4.1 --- Functional Testing vs. Structural Testing --- p.14Chapter 2.4.2 --- Scan-Based DfT --- p.15Chapter 2.4.3 --- Pseudo-Functional Testing --- p.17Chapter 2.5 --- Timing Error Tolerance --- p.19Chapter 2.5.1 --- Timing Error Detection --- p.19Chapter 2.5.2 --- Timing Error Recover --- p.20Chapter 3 --- Timing-Independent False Path Identification --- p.23Chapter 3.1 --- Introduction --- p.23Chapter 3.2 --- Preliminaries and Motivation --- p.26Chapter 3.2.1 --- Motivation --- p.27Chapter 3.3 --- False Path Examination Considering Illegal States --- p.28Chapter 3.3.1 --- Path Sensitization Criterion --- p.28Chapter 3.3.2 --- Path-Aware Illegal State Identification --- p.30Chapter 3.3.3 --- Proposed Examination Procedure --- p.31Chapter 3.4 --- False Path Identification --- p.32Chapter 3.4.1 --- Overall Flow --- p.34Chapter 3.4.2 --- Static Implication Learning --- p.35Chapter 3.4.3 --- Suspicious Node Extraction --- p.36Chapter 3.4.4 --- S-Frontier Propagation --- p.37Chapter 3.5 --- Experimental Results --- p.38Chapter 3.6 --- Conclusion and Future Work --- p.42Chapter 4 --- PSN Aware Pseudo-Functional Delay Testing --- p.43Chapter 4.1 --- Introduction --- p.43Chapter 4.2 --- Preliminaries and Motivation --- p.45Chapter 4.2.1 --- Motivation --- p.46Chapter 4.3 --- Proposed Methodology --- p.48Chapter 4.4 --- Maximizing PSN Effects under Functional Constraints --- p.50Chapter 4.4.1 --- Pseudo-Functional Relevant Transitions Generation --- p.51Chapter 4.5 --- Experimental Results --- p.59Chapter 4.5.1 --- Experimental Setup --- p.59Chapter 4.5.2 --- Results and Discussion --- p.60Chapter 4.6 --- Conclusion --- p.64Chapter 5 --- In-Situ Timing Error Masking in Logic Circuits --- p.65Chapter 5.1 --- Introduction --- p.65Chapter 5.2 --- Prior Work and Motivation --- p.67Chapter 5.3 --- In-Situ Timing Error Masking with Approximate Logic --- p.69Chapter 5.3.1 --- Equivalent Circuit Construction with Approximate Logic --- p.70Chapter 5.3.2 --- Timing Error Masking with Approximate Logic --- p.72Chapter 5.4 --- Cost-Efficient Synthesis for InTimeFix --- p.75Chapter 5.4.1 --- Overall Flow --- p.76Chapter 5.4.2 --- Prime Critical Segment Extraction --- p.77Chapter 5.4.3 --- Prime Critical Segment Merging --- p.79Chapter 5.5 --- Experimental Results --- p.81Chapter 5.5.1 --- Experimental Setup --- p.81Chapter 5.5.2 --- Results and Discussion --- p.82Chapter 5.6 --- Conclusion --- p.85Chapter 6 --- Conclusion and Future Work --- p.86Bibliography --- p.10

Investigation into voltage and process variation-aware manufacturing test

Increasing integration and complexity in IC design provides challenges for manufacturing testing. This thesis studies how process and supply voltage variation influence defect behaviour to determine the impact on manufacturing test cost and quality. The focus is on logic testing of static CMOS designs with respect to two important defect types in deep submicron CMOS: resistive bridges and full opens. The first part of the thesis addresses testing for resistive bridge defects in designs with multiple supply voltage settings. To enable analysis, a fault simulator is developed using a supply voltage-aware model for bridge defect behaviour. The analysis shows that for high defect coverage it is necessary to perform test for more than one supply voltage setting, due to supply voltage-dependent behaviour. A low-cost and effective test method is presented consisting of multi-voltage test generation that achieves high defect coverage and test set size reduction without compromise to defect coverage. Experiments on synthesised benchmarks with realistic bridge locations validate the proposed method.The second part focuses on the behaviour of full open defects under supply voltage variation. The aim is to determine the appropriate value of supply voltage to use when testing. Two models are considered for the behaviour of full open defects with and without gate tunnelling leakage influence. Analysis of the supply voltage-dependent behaviour of full open defects is performed to determine if it is required to test using more than one supply voltage to detect all full open defects. Experiments on synthesised benchmarks using an extended version of the fault simulator tool mentioned above, measure the quantitative impact of supply voltage variation on defect coverage.The final part studies the impact of process variation on the behaviour of bridge defects. Detailed analysis using synthesised ISCAS benchmarks and realistic bridge model shows that process variation leads to additional faults. If process variation is not considered in test generation, the test will fail to detect some of these faults, which leads to test escapes. A novel metric to quantify the impact of process variation on test quality is employed in the development of a new test generation tool, which achieves high bridge defect coverage. The method achieves a user-specified test quality with test sets which are smaller than test sets generated without consideration of process variation

Application of Logic Synthesis Toward the Inference and Control of Gene Regulatory Networks

In the quest to understand cell behavior and cure genetic diseases such as cancer, the fundamental approach being taken is undergoing a gradual change. It is becoming more acceptable to view these diseases as an engineering problem, and systems engineering approaches are being deployed to tackle genetic diseases. In this light, we believe that logic synthesis techniques can play a very important role. Several techniques from the field of logic synthesis can be adapted to assist in the arguably huge effort of modeling cell behavior, inferring biological networks, and controlling genetic diseases. Genes interact with other genes in a Gene Regulatory Network (GRN) and can be modeled as a Boolean Network (BN) or equivalently as a Finite State Machine (FSM). As the expression of genes deter- mine cell behavior, important problems include (i) inferring the GRN from observed gene expression data from biological measurements, and (ii) using the inferred GRN to explain how genetic diseases occur and determine the ”best” therapy towards treatment of disease. We report results on the application of logic synthesis techniques that we have developed to address both these problems. In the first technique, we present Boolean Satisfiability (SAT) based approaches to infer the predictor (logical support) of each gene that regulates melanoma, using gene expression data from patients who are suffering from the disease. From the output of such a tool, biologists can construct targeted experiments to understand the logic functions that regulate a particular target gene. Our second technique builds upon the first, in which we use a logic synthesis technique; implemented using SAT, to determine gene regulating functions for predictors and gene expression data. This technique determines a BN (or family of BNs) to describe the GRN and is validated on a synthetic network and the p53 network. The first two techniques assume binary valued gene expression data. In the third technique, we utilize continuous (analog) expression data, and present an algorithm to infer and rank predictors using modified Zhegalkin polynomials. We demonstrate our method to rank predictors for genes in the mutated mammalian and melanoma networks. The final technique assumes that the GRN is known, and uses weighted partial Max-SAT (WPMS) towards cancer therapy. In this technique, the GRN is assumed to be known. Cancer is modeled using a stuck-at fault model, and ATPG techniques are used to characterize genes leading to cancer and select drugs to treat cancer. To steer the GRN state towards a desirable healthy state, the optimal selection of drugs is formulated using WPMS. Our techniques can be used to find a set of drugs with the least side-effects, and is demonstrated in the context of growth factor pathways for colon cancer