An extended class of sequential circuits with combinational test generation complexity

This paper presents a nonscan design-for-testability (DFT) method for register-transfer-level (RTL) circuits. We first introduce the notation to analyze the test generation complexity, as well as two classes of sequential circuits, namely: 1) the combinationally testable class and 2) the acyclically testable class. Then, we introduce a new class of linear-depth time-bounded circuits as one of the acyclically testable classes. The linear-depth time-bounded testability guarantees that the number of time frames required for any testable fault is bounded by a linear function of the number of flip-flops in the circuit during the test generation process. As one of the linear-depth time-bounded classes, we introduce a new class of RTL circuits, called the cycle-unrollable RTL circuits, which is shown to be linear depth time bounded. We propose a DFT method to make RTL circuits cycle unrollable and a test generation method for cycle-unrollable RTL circuits. Experimental results show that we can drastically reduce hardware overhead and test application time compared to the full-scan method and the method proposed by Ohtake Moreover, our proposed method can achieve 100% fault efficiency for gate-level single stuck-at faults in practical test generation time and allow at-speed testing.

Despite recent progress in automated test generation research, significant challenges remain for applying these techniques on large-scale software systems. These systems under test often require structurally complex test inputs within a large input domain. It is challenging to automatically generate a reasonable number of tests that are both legal and behaviorally-diverse to exercise these systems. Constraint-based test generation is an effective approach for generating structurally complex inputs for systematic testing. While this approach can typically generate large numbers of tests, it has limited scalability – tests generated are usually only up to a small bound on input size. Combinatorial test generation, e.g., pair-wise testing, is a more scalable approach but is challenging to apply on commercial software systems that require complex input structures that cannot be formed by using arbitrary combinations. This paper introduces comKorat, which unifies constraint-based generation of structurally complex tests with combinatorial testing. Specifically, comKorat integrates Korat and ACTS test generators to generate test suites for large scale software systems with structurally complex test inputs. We have successfully applied comKorat on four software applications developed at eBay and Yahoo!. The experimental results show that comKorat outperforms existing solutions in execution time and test coverage. Furthermore, comKorat found a total of 59 previously unknown bugs in the four applications.

According to a recent synthesis for testability proposal, a test function specified as a finite state machine with the same number of state variables as the given object machine, is incorporated into the state diagram prior to synthesis. Since a complete verification of the test machine is not practical, an often used heuristic sets and observes each state variable. The two machines share logic and a fault can result in partial or total loss of the test function. We show that the tests generated under the assumption that the entire test function is intact can become invalid. We propose a new method of synthesizing PLA-based finite state machines with fault tolerant test machines. Our approach eliminates testing of the test function. A constrained logic minimization phase insures that faults have predictable effect on the state diagram of the composite machine (object machine embedded with the test function). This allows effective use of the test function during test generation even in the presence of faults that effect both object and test machines. Only a combinational test generator is required for test generation. Each combinational vector is augmented by appropriate initialization and propagation sequences. Unlike prior approaches, ourO(log2 n) length test sequence isguaranteed to detect any targeted crosspoint fault. Experimental results on the MCNC Logic Synthesis Workshop finite state machine benchmark set are given as evidence of practicality of the proposed approach.

Full scan designs are widely used for their indisputable benefits of predictably high test coverage, diagnosis and debug. However, for high-performance designs the cost of scan - area and delay - is not acceptable and partial scan is used instead. Unfortunately, partial scan significantly increases test generation complexity. We define a structured partial scan design methodology and specific test generation enhancements, which significantly enhance test coverage and reduce test data and cycles. Selective design areas use special types of nonscan cells which can capture a value in the last few scan load cycles. Combinational test generation is extended to work with this structured partial scan design, resulting in higher coverage and fewer patterns. Experimental results on industrial designs show consistent testability benefits.

This paper presents an efficient automatic test pattern generation technique for loop-free circuits. A partial scan technique is used to convert a sequential circuit (finite state machine) with arbitrary feedback paths into a pipelined circuit for testing. Test generation for these modified circuits can be performed with a modified combinational automatic test pattern generator (ATPG), which is much faster than a sequential ATPG. A combinational model is obtained by replacing all flipflops by buffers. It is shown that a test vector for a fault in this model obtained by a combinational test generator can be expanded into a sequence of identical vectors to detect the same fault in the original sequential circuit. This technique may abort a few faults which can then be resolved with a sequential ATPG. Experiments on the ISCAS89 circuits show that only 30% to 70% of flipflops require scanning in larger circuits and 96% to 100% fault coverage for almost all the circuits without resorting to a sequential ATPG.

We present a technique for extracting functional (control/dataflow) information from register transfer level (RTL) controller/data path circuits and illustrate its use in design for hierarchical testability of these circuits. This testing procedure and design for testability (DFT) technique is general enough to handle RTL control flow intensive circuits like protocol handlers as well as data flow intensive circuits like digital filters. It makes the combined controller-data path highly testable and does not require any external behavioral information. This scheme has the advantages of low area/delay/power overheads (average of 3.2%, 0.9% and 4.1%, respectively, for benchmarks), high fault coverage (over 99% for most cases), very low test generation times (because it is independent of bit-width), and the advantage of at-speed testing. Experiments show a 2-to-4 (1-to-3) orders of magnitude test generation time advantage over an efficient gate-level sequential test generator (combinational test generator that assumes full scan).

Static tests are key in reducing the current high cost of testing analog and mixed-signal ICs. A new DC test generation technique for detecting catastrophic failures in this class of circuits is presented. To include the effect of tolerance of parameters during testing, the test generation problem is formulated as a minimax optimization problem, and solved iteratively as successive linear programming problems. An analytical fault modeling technique, based on manufacturing defect statistics is used to derive the fault list for the test generation. Using the technique presented here an efficient static test set for analog and mixed-signal ICs can be constructed, reducing both the test time and the packaging cost.

In this paper, we discuss the relationship between the test generation complexity for path delay faults (PDFs) and that for stuck-at faults (SAFs) in combinational and sequential circuits using the recently introduced τk-notation. On the other hand, we also introduce a class of cyclic sequential circuits that are easily testable, namely two-column distributive state-shiftable finite state machine realizations (2CD-SSFSM). Then, we discuss the relevant conjectures and unsolved problems related to the test generation for sequential circuits with PDFs under different clock schemes and test generation models.

Circuits that have an underlying acyclic topology are guaranteed to be combinational since feedback is necessary for sequential behavior. However, the reverse is not true, i,e., feedback is not a sufficient condition since there do exist combinational logic circuits that are cyclic. In fact, such combinational circuits occur often in bus structures in data paths. This class of circuits has largely been ignored by conventional combinational single-stuck-at fault test pattern generators which assume that the circuit topology is acyclic. There has not been a formal study of the test generation problem for these circuits. Also, no algorithms and tools exist for this purpose. In practice, test generation for these circuits is handled in an awkward manner, typically with poor fault coverage. This work provides, for the first time, a formal analysis of the test generation problem for these circuits. This analysis leads to a clear insight into generation of tests, as well as a classification of untestable faults for such circuits. We demonstrate that cyclic combinational circuits may have untestable faults that do not correspond to redundancies. This insight is then translated to a testing algorithm which has been implemented in the program RAM. RAM has been successful in providing complete or near complete coverage on a range of typical examples, which is significantly higher than that provided by conventional techniques. >

Considers polynomial time testability of combinational circuits generated by input decomposition, especially those generated by the logic synthesis tool FACTOR. First, the complexity of the fault detection problem in this class of circuits is explored using a stuck-at fault model. An O(2/sup k/m) algorithm for detecting a single stuck-at fault is given that is faster than the O(16/sup k/m), previously reported best algorithm proposed by Fujiwara(1990), where k is the number of inputs in a subcircuit and m the number of signal lines in the circuit. Efficient, polynomial time algorithms are described for generating a test set for all single stuck-at faults in the circuit. The basic strategy is to eliminate backtracks during line justification by constructing tables or vector sets in each subcircuit, which makes the fault propagation procedure very simple and eventually results in an efficient test generation procedure. This presentation of efficient polynomial time test generation algorithms for FACTOR-generated circuits is important, since it shows that it is possible to synthesize circuits that are optimized for area and are polynomial time testable at the same time. >

Today, VLSI design has progressed to a stage where it needs to incorporate methods of testing circuits. The Automatic Test Pattern Generation (ATPG) is a very attractive method and feasible on almost any combinational and sequential circuit. Currently available automatic test pattern generators (ATPGs) generate test sets that may be excessively long. Because a cost of testing depends on the test length, compaction techniques have been used to reduce that length. The motivation for studying test compaction is twofold. Firstly, by reducing the test sequence length, the memory requirements during the test application and the test application time are reduced. Secondly, the extent of test compaction possible for deterministic test sequences indicates that test pattern generators spend a significant amount of time generating test vectors that are not necessary. The compacted test sequences provide a target for more efficient deterministic test generators. Two types of compaction techniques exist: dynamic and static. The dynamic test sequence compaction performs compaction concurrently with the test generation process and often requires modification of the test generator. The static test sequence compaction is done in a post-processing step to the test generation and is independent of the test generation algorithm and process. In the thesis, a new idea for static compaction of test sequences for synchronous sequential circuits has been proposed. Our new method - SUSEM (Set Up Sequence Elimination Method) uses the circuit state information to eliminate some setup sequences for the target faults and consequently reduce the test sequence length. The technique has been used for the test sequences generated by HITEC test generator. ISCAS89 benchmark circuits were used in our experiments, for some circuits which have a large number of target faults and relatively small number of flip-flops, the very significant compactions have been obtained. The more important is that this method can be used to improve the test generation procedure unlike most static compaction methods which blindly or randomly remove parts of test vectors and cannot be used to improve the test generators.

An efficient sequential circuit test generation algorithm is presented. The algorithm is based on PODEM and uses a nine-valued logic model. Among the novel features of the algorithm are use of an initial time-frame algorithm and correct implementation of a solution to the previous state information problem. The initial time-frame algorithm determines the number of time-frames required to excite the fault under test and the number of time-frames required to observe the excited fault. This step saves the test generator from doing unnecessary search in the input space. Test generation is done strictly in forward time. The algorithm saves good machine circuit state after test generation to aid in future test generation. Faulty machine state is set to unknown whenever test generation for a fault is begun. This solves the previous state information problem, which has often been ignored by existing test generators. >

Combining functional and structural approaches in test generation for digital systems

PRECISE, Photonic hybRid EleCtromagnetIc SolvEr, is a Matlab-based library to model large and complex photonic integrated circuits. Each circuit is modularly described in terms of waveguide segments connected through multi-port nodes. Linear, nonlinear, and dynamical phenomena are simulated by solving the system of differential equations describing the effect to be considered. By exploiting the steady-state approximation of the electromagnetic field within each node device, the library can handle large and complex circuits even on desktop PCs. We show that the steady-state assumption is fulfilled in a broad number of applications and we compare its accuracy with an analytical model (coupled mode theory) and experimental results. PRECISE is highly modular and easily extensible to handle equations different from those already implemented and is, thus, a flexible tool to model the increasingly complex photonic circuits.

Due to the complexity of test generation for stuck-at-faults in synchronous sequential circuits and the permanently increasing problem-size, algorithms solving this problem cannot work with acceptable CPU-time, even on computer systems with very high performance. Relating to this context this paper presents a new testability analysis guiding algorithms for sequential test generation. This testability analysis consists of two separated parts: First, a new technique for the detection of untestable stuck-at-faults; second, heuristics used to guide the decision process in test generation algorithms. Experimental results of sequential benchmark circuits allow us to conclude that our testability analysis provides less CPU-time for sequential test generation than other well-known testability analysis tools. >