Görschwin Fey

On Acceleration of SAT-Based ATPG for Industrial Designs

Due to the rapidly growing size of integrated circuits, there is a need for new algorithms for automatic test pattern generation (ATPG). While classical algorithms reach their limit, there have been recent advances in algorithms to solve Boolean Satisfiability (SAT). Because Boolean SAT solvers are working on conjunctive normal forms (CNFs), the problem has to be transformed. During transformation, relevant information about the problem might get lost and, therefore, is not available in the solving process. In this paper, we present a technique that applies structural knowledge about the circuit during the transformation. As a result, the size of the problem instances decreases, as well as the run time of the ATPG process. The technique was implemented, and experimental results are presented. The approach was combined with the ATPG framework of NXP Semiconductors. It is shown that the overall performance of an industrial framework can significantly be improved. Further experiments show the benefits with regard to the efficiency and robustness of the combined approach.

Automatic Fault Localization for Property Checking

We present an efficient fully automatic approach to fault localization for safety properties stated in linear temporal logic. We view the failure as a contradiction between the specification and the actual behavior and look for components that explain this discrepancy. We find these components by solving the satisfiability of a propositional Boolean formula. We show how to construct this formula and how to extend it so that we find exactly those components that can be used to repair the circuit for a given set of counterexamples. Furthermore, we discuss how to efficiently solve the formula by using the proper decision heuristics and simulation-based preprocessing. We demonstrate the quality and efficiency of our approach by experimental results.

Synthesis of fully testable circuits from BDDs

We present a technique to derive fully testable circuits under the stuck-at fault model (SAFM) and the path-delay fault model (PDFM). Starting from a function description as a binary decision diagram, the netlist is generated by a linear time mapping algorithm. Only one additional input and one inverter are needed to achieve 100% testable circuits under SAFM and PDFM. Experiments are given to show the advantages of the technique.

Automatic fault localization for property checking

We present an efficient, fully automatic approach to fault localization for safety properties stated in linear temporal logic. We view the failure as a contradiction between the specification and the actual behavior and look for components that explain this discrepancy. We find these components by solving the satisfiability of a propositional Boolean formula. We show how to construct this formula and how to extend it so that we find exactly those components that can be used to repair the circuit for a given set of counterexamples. Furthermore, we discuss how to efficiently solve the formula by using the proper decision heuristics and simulation based preprocessing. We demonstrate the quality and efficiency of our approach by experimental results.

Automatic generation of complex properties for hardware designs

Property checking is a promising approach to prove the correctness of todays complex designs. However, in practice this requires the formulation of formal properties which is a time consuming and non-trivial task. Therefore the acceptance and efficiency of formal verification techniques can be raised by an automated support for formulating design properties. In this paper we propose a new methodology to automatically generate complex properties for a given design. The tool, Dianosis, implements this methodology by analyzing a simulation trace. The extracted properties describe the abstract design behavior and are presented in a format that is easy to read and can be added to the set of properties used for formal or assertion-based verification. We provide experimental results on industrial hardware designs that show the effectiveness of Dianosis and motivate the practical use.

WoLFram- A Word Level Framework for Formal Verification

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.

Cost-efficient block verification for a UMTS up-link chip-rate coprocessor

ASIC designs for future communication applications cannot be simulated exhaustively. Formal property checking is a powerful technology to overcome the limitations of current functional verification approaches. The paper reports on a large-scale experiment employing the CVE property checker for verifying the block-level functional correctness of a large ASIC. This new verification methodology achieves substantial quality and productivity gains. The two biggest advantages are: 1) coding and verification can be done in parallel; and 2) the whole state space of a test case will be verified in a single run. Formal property checking simplifies and shortens the functional verification of large-scale ASICs at least in the same order of magnitude as static timing analysis did for timing verification.

SWORD: A SAT like prover using word level information

Solvers for Boolean Satisfiabilily (SAT) are state-of-the-art to solve verification problems. But when arithmetic operations are considered, the verification performance degrades with increasing data-path width. Therefore, several approaches that handle a higher level of abstraction have been studied in the past. But the resulting solvers are still not robust enough to handle problems that mix word level structures with bit level descriptions. In this paper, we present the satisfiability solver SWORD — a SAT like solver that facilitates word level information. SWORD represents the problem in terms of modules that define operations over bit vectors. Thus, word level information and structural knowledge become available in the search process. The experimental results show that on our benchmarks SWORD is more robust than Boolean SAT, K⋆BMDs or SMT.

Minimizing the number of paths in BDDs: Theory and algorithm

The complexity of circuit and systems design increases rapidly. Therefore, a main focus of research in the area of electronic-design automation are efficient algorithms and data structures. Among these, binary decision diagrams (BDDs) have been used in a wide variety of applications and were intensively studied from a theoretical point of view. But mostly, when complexity issues were considered, only the number of nodes in a BDD has been analyzed. Here, we study minimizing the number of paths in BDDs from a theoretical and a practical point of view. Connections to different areas in computer-aided design are outlined, theoretical studies are carried out, and an algorithm to minimize the number of paths is presented. Experimental results show the efficiency of the algorithm.

PASSAT: efficient SAT-based test pattern generation for industrial circuits

Automatic test pattern generation (ATPG) based on Boolean satisfiability (SAT) has been proposed as an alternative to classical search algorithms. SAT-based ATPG turned out to be more robust and more effective by formulating the problem as a set of equations. In this paper, we present an efficient ATPG algorithm that makes use of powerful SAT-solving techniques. Problem specific heuristics are applied to guide the search. In contrast to previous SAT-based algorithms, the new approach can also cope with tri-states. The algorithm has been implemented as the tool PASSAT. Experimental results on large industrial circuits are given to demonstrate the quality and efficiency of the algorithm.