Scalable algorithms for software based self test using formal methods

textTransistor scaling has kept up with Moore's law with a doubling of the number of transistors on a chip. More logic on a chip means more opportunities for manufacturing defects to slip in. This, in turn, has made processor testing after manufacturing a significant challenge. At-speed functional testing, being completely non-intrusive, has been seen as the ideal way of testing chips. However for processor testing, generating instruction level tests for covering all faults is a challenge given the issue of scalability. Data-path faults are relatively easier to control and observe compared to control-path faults. In this research we present a novel method to generate instruction level tests for hard to detect control-path faults in a processor. We initially map the gate level stuck-at fault to the Register Transfer Level (RTL) and build an equivalent faulty RTL model. The fault activation and propagation constraints are captured using Control and Data Flow Graphs of the RTL as a Liner Temporal Logic (LTL) property. This LTL property is then negated and given to a Bounded Model Checker based on a Bit-Vector Satisfiability Module Theories (SMT) solver. From the counter-example to the property we can extract a sequence of instructions that activates the gate level fault and propagates the fault effect to one of the observable points in the design. Other than the user supplying instruction constraints, this approach is completely automatic and does not require any manual intervention. Not all the design behaviors are required to generate a test for a fault. We use this insight to scale our previous methodology further. Underapproximations are design abstractions that only capture a subset of the original design behaviors. The use of RTL for test generation affords us two types of under-approximations: bit-width reduction and operator approximation. These are abstractions that perform reductions based on semantics of the RTL design. We also explore structural reductions of the RTL, called path based search, where we search through error propagation paths incrementally. This approach increases the size of the test generation problem step by step. In this way the SMT solver searches through the state space piecewise rather than doing the entire search at once. Experimental results show that our methods are robust and scalable for generating functional tests for hard to detect faults.Electrical and Computer Engineerin

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

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

Efficient Path Delay Test Generation with Boolean Satisfiability

This dissertation focuses on improving the accuracy and efficiency of path delay test generation using a Boolean satisfiability (SAT) solver. As part of this research, one of the most commonly used SAT solvers, MiniSat, was integrated into the path delay test generator CodGen. A mixed structural-functional approach was implemented in CodGen where longest paths were detected using the K Longest Path Per Gate (KLPG) algorithm and path justification and dynamic compaction were handled with the SAT solver. Advanced techniques were implemented in CodGen to further speed up the performance of SAT based path delay test generation using the knowledge of the circuit structure. SAT solvers are inherently circuit structure unaware, and significant speedup can be availed if structure information of the circuit is provided to the SAT solver. The advanced techniques explored include: Dynamic SAT Solving (DSS), Circuit Observability Don’t Care (Cir-ODC), SAT based static learning, dynamic learnt clause management and Approximate Observability Don’t Care (ACODC). Both ISCAS 89 and ITC 99 benchmarks as well as industrial circuits were used to demonstrate that the performance of CodGen was significantly improved with MiniSat and the use of circuit structure

A survey of scan-capture power reduction techniques

With the advent of sub-nanometer geometries, integrated circuits (ICs) are required to be checked for newer defects. While scan-based architectures help detect these defects using newer fault models, test data inflation happens, increasing test time and test cost. An automatic test pattern generator (ATPG) exercise’s multiple fault sites simultaneously to reduce test data which causes elevated switching activity during the capture cycle. The switching activity results in an IR drop exceeding the devices under test (DUT) specification. An increase in IR-drop leads to failure of the patterns and may cause good DUTs to fail the test. The problem is severe during at-speed scan testing, which uses a functional rated clock with a high frequency for the capture operation. Researchers have proposed several techniques to reduce capture power. They used various methods, including the reduction of switching activity. This paper reviews the recently proposed techniques. The principle, algorithm, and architecture used in them are discussed, along with key advantages and limitations. In addition, it provides a classification of the techniques based on the method used and its application. The goal is to present a survey of the techniques and prepare a platform for future development in capture power reduction during scan testing

UA2TPG: An untestability analyzer and test pattern generator for SEUs in the configuration memory of SRAM-based FPGAs

This paper presents UA2TPG, a static analysis tool for the untestability proof and automatic test pattern generation for SEUs in the configuration memory of SRAM-based FPGA systems. The tool is based on the model-checking verification technique. An accurate fault model for both logic components and routing structures is adopted. Experimental results show that many circuits have a significant number of untestable faults, and their detection enables more efficient test pattern generation and on-line testing. The tool is mainly intended to support on-line testing of critical components in FPGA fault-tolerant systems