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

Incremental bounded model checking for embedded software

Program analysis is on the brink of mainstream usage in embedded systems development. Formal verification of behavioural requirements, finding runtime errors and test case generation are some of the most common applications of automated verification tools based on bounded model checking (BMC). Existing industrial tools for embedded software use an off-the-shelf bounded model checker and apply it iteratively to verify the program with an increasing number of unwindings. This approach unnecessarily wastes time repeating work that has already been done and fails to exploit the power of incremental SAT solving. This article reports on the extension of the software model checker CBMC to support incremental BMC and its successful integration with the industrial embedded software verification tool BTC EMBEDDED TESTER. We present an extensive evaluation over large industrial embedded programs, mainly from the automotive industry. We show that incremental BMC cuts runtimes by one order of magnitude in comparison to the standard non-incremental approach, enabling the application of formal verification to large and complex embedded software. We furthermore report promising results on analysing programs with arbitrary loop structure using incremental BMC, demonstrating its applicability and potential to verify general software beyond the embedded domain

Exploiting Resolution-based Representations for MaxSAT Solving

Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver in order to find an optimal solution. In particular, several algorithms take advantage of the ability of SAT solvers to identify unsatisfiable subformulas. Usually, these MaxSAT algorithms perform better when small unsatisfiable subformulas are found early. However, this is not the case in many problem instances, since the whole formula is given to the SAT solver in each call. In this paper, we propose to partition the MaxSAT formula using a resolution-based graph representation. Partitions are then iteratively joined by using a proximity measure extracted from the graph representation of the formula. The algorithm ends when only one partition remains and the optimal solution is found. Experimental results show that this new approach further enhances a state of the art MaxSAT solver to optimally solve a larger set of industrial problem instances

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 Methodology for Evaluating Artifacts Produced by a Formal Verification Process

The goal of this study is to produce a methodology for evaluating the claims and arguments employed in, and the evidence produced by formal verification activities. To illustrate the process, we conduct a full assessment of a representative case study for the Enabling Technology Development and Demonstration (ETDD) program. We assess the model checking and satisfiabilty solving techniques as applied to a suite of abstract models of fault tolerant algorithms which were selected to be deployed in Orion, namely the TTEthernet startup services specified and verified in the Symbolic Analysis Laboratory (SAL) by TTTech. To this end, we introduce the Modeling and Verification Evaluation Score (MVES), a metric that is intended to estimate the amount of trust that can be placed on the evidence that is obtained. The results of the evaluation process and the MVES can then be used by non-experts and evaluators in assessing the credibility of the verification results

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