When a model does not satisfy a given specification, a counterexample is produced by the model checker to demonstrate the failure. A user must then examine the counterexample trace, in order to visually identify the failure that it demonstrates. If the trace is long, or the specification is complex, finding the failure in the trace becomes a non-trivial task. In this paper, we address the problem of analyzing a counterexample trace and highlighting the failure that it demonstrates. Using the notion of causality , introduced by Halpern and Pearl, we formally define a set of causes for the failure of the specification on the given counterexample trace. These causes are marked as red dots and presented to the user as a visual explanation of the failure. We study the complexity of computing the exact set of causes, and provide a polynomial-time algorithm that approximates it. This algorithm is implemented as a feature in the IBM formal verification platform RuleBase PE, where these visual explanations are an integral part of every counterexample trace. Our approach is independent of the tool that produced the counterexample, and can be applied as a light-weight external layer to any model checking tool, or used to explain simulation traces.

/pdf/explaining-counterexamples-using-causality-3e2yod3mru.pdf

Explaining Counterexamples Using Causality

As contemporary very large scale integration designs grow in complexity, design debugging has rapidly established itself as one of the largest bottlenecks in the design cycle today. Automated debug solutions such as those based on Boolean satisfiability (SAT) enable engineers to reduce the debug effort by localizing possible error sources in the design. Unfortunately, adaptation of these techniques to industrial designs is still limited by the performance and capacity of the underlying engines. This paper presents a novel formulation of the debugging problem using MaxSAT to improve the performance and applicability of automated debuggers. Our technique not only identifies errors in the design but also indicates when the bug is excited in the error trace. MaxSAT allows for a simpler formulation of the debugging problem, reducing the problem size by 80% compared to a conventional SAT-based technique. Empirical results demonstrate the effectiveness of the proposed formulation as run-time improvements of 4.5 × are observed on average. This paper introduces two performance improvements to further reduce the time required to find all error sources within the design by an order of magnitude.

/pdf/automated-design-debugging-with-maximum-satisfiability-2jb131bdlt.pdf

Automated Design Debugging With Maximum Satisfiability

The localisation of faults in integrated circuits is a challenging problem and a dominating factor in the overall verification effort. Electrical bugs, in particular, surface only in the fabricated prototypes, leading to behaviour deviating from the golden model. Limited observability complicates their localisation: Logging mechanisms such as trace buffers allow us to retain only a limited execution history. A symbolic analysis of the RTL design can find discrepancies between the values recorded in the trace buffer and the intended behaviour. Contemporary MAX-SAT solvers are then able to identify a maximal subset of the RTL design that is consistent with the observed behaviour. The elements in the complement of this subset represent potential locations of the fault. The scalability of contemporary decision procedures dictates the size of a window of execution cycles which we can analyse using symbolic techniques. Current MAX-SAT-based fault localisation techniques require this window to span the fault as well as the error it causes. To address the scalability issues resulting from large window sizes, we propose to slide a smaller window along the temporal axis, constraining it with the information recorded in the trace buffer for the respective execution cycles. In this scenario, the localisation attempt may fail: The limited information provided by the trace buffer may be insufficient to pin down the exact temporal and spatial location of the fault. We propose to use backbones to identify information that can be propagated across sliding windows. The backbone of a symbolic representation of a circuit is the set of signals that are immutable under the given constraints (e.g., the output and trace buffer values). This additional information has several benefits: Firstly, it may be instrumental in locating the fault. Secondly, it may enable a reduction of the size of the of trace buffers and the sliding window. Our preliminary experimental results demonstrate that the use of backbones allows us to reduce the size of the sliding windows or the trace buffer.

Post-silicon fault localisation using maximum satisfiability and backbones

This book covers recent advances in the field of logic synthesis and design, including Boolean Matching, Logic Decomposition, Boolean satisfiability, Advanced Synthesis Techniques and Applications of Logic Design. All of these topics are valuable to CAD engineers working in Logic Design, Logic Optimization, and Verification. Engineers seeking opportunities for optimizing VLSI integrated circuits will find this book as an invaluable reference, since there is no existing book that covers this material in a systematic fashion.

Advanced Techniques in Logic Synthesis, Optimizations and Applications

Due to high computational costs of formal verification on pure Boolean level, proof techniques on the word level, like Satisfiability Modulo Theories (SMT), were proposed. Verification methods originally based on Boolean satisfiability (SAT) can directly benefit from this progress. In this work we present the word level framework WoLFram that enables the development of applications for formal verification of systems independent of the underlying proof technique. The framework is partitioned into an application layer, a core engine and a back-end layer. A wide range of applications is implemented, e.g.~equivalence and property checking including algorithms for coverage/property analysis, debugging and robustness checking. The back-end supports Boolean as well as word level techniques, like SMT and Constraint Solving (CSP). This makes WoLFram a stable backbone for the development and quick evaluation of emerging verification techniques.

/pdf/wolfram-a-word-level-framework-for-formal-verification-53omxx9w0j.pdf

WoLFram- A Word Level Framework for Formal Verification

Due to the increasing complexity of today's circuits a high degree of automation in the design process is mandatory. The detection of faults and design errors is supported quite well using simulation or formal verification. But locating the fault site is typically a time consuming manual task. Techniques to automate debugging and diagnosis have been proposed. Approaches based on Boolean Satisfiability (SAT) have been demonstrated to be very effective. In this work debugging on the gate level is considered. Unsatisfiable cores contained in a SAT instance for debugging are used (1) to determine all suspects, and (2) to speed-up the debugging process. In comparison to standard SAT-based debugging, the experimental results show a significant speed-up for debugging multiple faults.

/pdf/using-unsatisfiable-cores-to-debug-multiple-design-errors-2cbiamcbis.pdf

Using unsatisfiable cores to debug multiple design errors

Continuously shrinking feature sizes cause an increasing vulnerability of digital circuits. Manufacturing failures and transient faults may tamper the functionality. Automated support is required to analyze the fault tolerance of circuits. In this paper, Robu Check is presented - a design tool to analyze the fault tolerance of digital circuits. Engines based on simulation and formal methods are integrated to identify components that require additional fault protection. Consequently, an overall estimation of fault tolerance of the circuit is determined.

/pdf/robucheck-a-robustness-checker-for-digital-circuits-4hcpwxrruy.pdf

RobuCheck: A Robustness Checker for Digital Circuits

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Using unsatisfiable cores to debug multiple design errors

RobuCheck: A Robustness Checker for Digital Circuits