Critical path tracing in sequential circuits

~ NJ 07974 Abstract - This paper addresses the problem of simukating transition faults in synchronous sequential circuits. After presenting the concept of the transition fault modell for sequential circuits, we present a fault simulation algorithm for transition faults. The algorithm is a modification of PROOFS, a parallel, differential fault simulation algorithm for stuck faults. A novel fault injection technique is pro- posed. Experimental results show that neither a comprehen- sive functional verification sequence nor a test sequence gen- erated by a sequential circuit test generator for stucck-at faults produces a high fault coverage for transition faults. and finite state machine (FSM) synthesis for delay testabil- ity was adtlressedl. A known reset state is required. The method has limited capability of handling large circuits, because it Icquires the extraction of the complete or partial state transition graph. The approach suggested in 1131 assumes that the circuit is fault-free in the initialization and fault propagation phases. This suggestion is valid if the clock is applied alt a lower speed during the initialization and the fault propagation phases and is applied at a rated speed during the fault activation phase. Slow clock for ini- tialization ,and fault propagation is also assumed in (12). To the author's Icnowledge, no delay-fault simulator €or sequential circuits has been reported before. In this paper, we address the problem of simulating transition faults in sequential circuits. We first enhance the transition fault model for the gate-delay faults and the stuck-open faults in synchronous sequential circuits. We assume the input vectors and clock are applied at speed and at a fixed interval during test application. The primary outputs are: also observed at a fixed interval. We use a transition fault of size n clock cycles to model the defects that cause im extra delay of n clock cycles to a transition. We present a fault simulation algorithm for the proposed fault model. Fault simulation results on the ISCAS-89 sequential benchmark circuits are presented in Section 5.

The paper presents a concept of single event equivalence to be used in the sequential circuit fault simulator. The concept dynamically identifies the equivalent faults for a simulated pattern. It combines advantages of the fanout-free region, critical path tracing and the dominator concept, which were applicable only to combinational circuit fault simulation. The implemented fault simulator, SEESIM, based on the concept, demonstrated a performance superior to that of a state-of-the-art concurrent fault simulator, and comparable to that of parallel-pattern single-fault propagation simulators. It requires a minimal amount of memory and, because of its simplicity, can be easily extended to multilogic or higher level simulation.

TPG for synchronous sequential circuits has received wide attention over the last two decades, yet unlike for (full-scan) combinational circuits, for many sequential benchmark circuits 100% fault efficiency still cannot be reached. This illustrates the complexity of sequential circuit ATPG. The huge search space, which exists during sequential circuit TPG, is the main reason for this complexity. Powerful techniques and heuristics are required to cope with this search space. One way to reduce the search space is the detection of illegal states. These states cannot be justified with an initialization sequence. In this paper, we propose new techniques to find illegal states and to remove the over-specification of these states by searching common fractions in the list of illegal states. Experimental results demonstrate the importance of an as complete as possible illegal state list: Higher fault efficiencies are reached for the sequential ISCAS'89 circuits (1989) and industrial circuits, together with a large reduction of CPU time.

A reliable method for delay fault diagnosis, based on critical path tracing from symbolic simulation of the fault-free circuit, is presented. It does not require timing evaluations and may be very accurate. The diagnosis method consists of simulation of the fault-free circuit with a six-valued logic algebra and a tracing of critical paths from primary outputs to primary inputs. The proposed method is an alternative to fault simulation. It requires no delay size based fault models and considers only the fault-free circuit. Consequently, this approach is faster, reliable, and requires less memory than conventional fault simulation. To improve the diagnosis accuracy, the concept of sensitive lines has been developed. Based on the method presented, a fast algorithm has been implemented in C++ on a SUN-SPARC workstation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Many applications produce acceptable results when their underlying computations are executed in an approximate manner. For such applications, approximate circuits enable hardware implementations that exhibit improved efficiency for a given quality. Previous efforts have largely focused on the design of approximate combinational logic blocks such as adders and multipliers. In practice, however, designers are concerned with the quality of outputs generated by a sequential circuit after several cycles of computation, rather than an embedded combinational block. We propose ASLAN (Automatic methodology for Sequential Logic ApproximatioN), the first effort towards the synthesis of approximate sequential circuits. Given a sequential circuit and an output quality constraint, ASLAN creates an approximate version of the circuit that consumes lower energy, while meeting the specified quality bound. The key challenges in approximating sequential circuits are (i) to model how errors due to approximations are generated, re-circulate through the combinational logic over multiple cycles of operation, and eventually impact quality of the final output, and (ii) to select the most beneficial approximations, i.e., those that result in higher energy savings for smaller impact on quality. ASLAN addresses the first challenge by constructing a virtual Sequential Quality Constraint Circuit (SQCC) and utilizing formal verification techniques to ensure that the selected approximations meet the quality constraint. To address the second challenge, ASLAN identifies combinational blocks in the sequential circuit that are amenable to approximation, generates local quality-energy trade-off curves for them, and uses a gradient-descent approach to iteratively approximate the entire sequential circuit. We used ASLAN to automatically synthesize approximate versions of ten sequential benchmarks, resulting in energy reductions of 1.20X-2.44X for tight quality constraints, and 1.32X-4.42X for moderate quality constraints. We present case studies of using the approximate circuits generated by ASLAN in two popular applications - MPEG Encoding and K-Means Clustering - obtaining 1.32X energy savings with 0.5% PSNR degradation, and 1.26X energy savings with 0.8% increase in mean cluster radius, respectively.

In the first part of the chapter, an introduction to the problem of logic level fault simulation is given together with the overview of existing fault simulation techniques. The remaining part of the chapter describes a new approach to fault simulation based on exact critical path tracing to conduct fault analysis in logic circuits. A circuit topology driven computational model is presented which allows not only to cope with complex structures of nested reconvergent fan-outs but also to carry out the fault reasoning for many test patterns concurrently. To achieve the speed-up of backtracing, the circuit is simulated on higher than traditional gate level. As components of the circuit network, fan-out free regions of maximum size are considered, and they are represented by structurally synthesized BDDs. The latter allow to reduce the number of internal variables in the computation model, and therefore to process the whole circuit faster than on the flat gate-level. The method is explained first, for the stuck-at fault model, and then generalized for an extended class of functional fault model covering the conditional stuck-at and transition faults. The method can be used for simulating permanent faults in combinational circuits, and transient or intermittent faults both in combinational and sequential circuits with the goal of selecting malicious faults for injecting into fault tolerant systems to evaluate their dependability. Experimental results are included to give an idea how efficiently the method works with different fault classes.

A study is made of single-fault fault collapsing in sequential logic circuits. Two major phenomena, self-hiding (SH) and delayed reconvergence (DR), which arise from the existence of feedback paths and storage elements in sequential circuits, are analyzed and found to cause the dominance relationship which is valid in combinational circuits but no longer valid in sequential circuits. A fault-collapsing procedure is proposed to collapse faults in sequential circuits. It first collapses faults in the non-SAD (self-hiding and delayed-reconvergence) gates of the combinational part of the sequential circuit and then further collapses faults by identifying the prime fan-out branches. Finally, it collapses faults in feedback lines. The collapsed faults constitute a sufficient representative set of prime faults.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The paper shows an influence of a choice of autonomous testing structure on fault coverage in synchronous digital sequential circuit testing. In order to increase testability of sequential circuit during testing, its memory module usually undergoes a disconnection. At the time the testing structure gains access to no-primary output of the testing circuit. The circuit undergoes transformation into combinational circuit. A possibility of disconnection of a memory module results from including of multifunctional registers which execute a circuit memory function. It turns out that high fault coverage may often be gained without disconnection of the module. Thus, it is not necessary to apply such registers. Therefore the complexity of circuit is limited as far as a circuit area overhead for its application and additional mode control during its work are concerned. Nevertheless, it is not always possible. Even partial disconnection of memory modules during testing phase enables to increase fault coverage due to increasing circuit testability. Simulation studies carried out on a considerate amount of ISCAS'89 testing circuits set show rightness of introduced conception of sequential circuits testing without interference with its memory function. An important factor enabling suggested approach is an adequate choice of autonomous testing structure.

A fault simulator for large synchronous sequential circuits is presented in this paper. There are four key ideas to the fault simulator. (1) It uses the critical path tracing method to screen out the single event faults that need not map into equivalent stem faults. (2) It uses the single fault propagation method to map the traced single event faults into equivalent stem faults. (3) All the multiple event faults are dynamically ordered for each test pattern such that the faults with the same faulty effects can be put into the same packet, so as to reduce the number of events created during simulation. (4) All the packets are propagated simultaneously; therefore, each gate is simulated only once for each test pattern, and while propagating packets, equivalent stem faults are also inserted into the packets and propagated as well. A memory sharing technique is used to reduce the memory overhead. Experimental results show that our fault simulator runs faster than PROOFS, HOPE, and improved HOPE (HOPE1.1) for large synchronous sequential benchmark circuits.

Retiming is an effective technique to optimize the performance of synchronous sequential circuits. This paper proposes a method to improve the effectiveness of retiming by transforming the sequential circuit. Bottlenecks which prevent retiming to achieve a desired clock period are identified. Conditions to eliminate the retiming bottlenecks are derived. These conditions are satisfied by a process of identifying sub-circuits and satisfying a set of timing constraints on the sub-circuits. The transformed circuit, which satisfies the timing constraints, can be retimed to achieve the desired clock period. If the original circuit has its initial state specified, our method always generates the final circuit with an equivalentinitial state. Experimental results on a variety of sequential benchmark circuits demonstrate significant performance improvement.

The authors discuss possibilities of delay fault diagnosis based on fault simulation. They detail the proposed approach based on critical path tracing. A path tracing process is presented with information provided by a logic simulation. Due to the limitations induced by such a simulation, a reliable approach is described based on a six-valued logic simulation. It requires no delay size based fault models and considers only the fault-free circuit. This method is an alternative to fault simulation based approaches and provides perfectly reliable results. It does not require timing evaluations and can be very accurate. >

We study storage schemes for test patterns and test responses of combinational and synchronous sequential circuits which are tested off-line by a tester. These storage schemes provide new objectives for test compaction beyond the need to reduce the test set size as much as possible. We report on several postprocessing methods to reduce the storage requirements of a given test set and present experimental evidence pointing to the possibility of reducing the storage requirements by using appropriate compaction objectives during test generation.

An approach to logic synthesis of digital synchronous sequential circuits is presented. Algorithms are described for minimizing the area of synchronous combinational and/or sequential circuits under cycle time constraints and for minimizing the cycle time under area constraints. It is shown how to optimize concurrently the circuit equations and the register position by a set of algorithms based on logic transformations. An implementation of the algorithms in the program Minerva is described, and experimental results are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new approach is presented to logic synthesis of digital synchronous sequential circuits. The authors describe algorithms for minimizing (i) the area of synchronous combinational and/or sequential circuits under cycle time constraints, and (ii) the cycle time under area constraints. Previous approaches attacked this problem by separating the combinational logic from the registers and by applying circuit transformations to the combinational component only. The authors show instead how to optimize concurrently the circuit equations and the register position. This method is novel and can achieve results that are at least as good as those obtained by previous methods. A computer implementation of the algorithms in the Minerva program is described. >

Field Programmable Gate Array (FPGA) technology is rapidly gaining traction in a wide range of applications. Nonetheless, FPGAs still require long design and debug cycles. To debug hardware circuits, trace-based instrumentation is inserted into the design that enables capturing data during the circuit execution into on-chip memories for later offline analysis. Since on-chip memories are limited, a trigger circuitry is used to only record data related to specific events during the execution. However, during debugging, a circuit recompilation is required on modifying these instruments. This can be very slow, reducing debug productivity. In this article, we propose a non-intrusive and rapid triggering solution with a tailored overlay fabric and mapping algorithm that seeks to enable fast debug iterations without performing a recompilation. This overlay is specialized for small combinational and sequential circuits with a single output; such circuits are typical of common trigger functions. We present an adaptive strategy to construct the overlay fabric using spare FPGA resources at compile time. At debug time, our proposed trigger mapping algorithms adapt to this specialized overlay to rapidly implement combinational and sequential trigger circuits. Our results show that the overlay fabric can be reconfigured to map different triggering scenarios in less than 40s instead of recompiling the circuit during debug iterations, increasing debug productivity.