Critical Path Selection Research Articles

Aging-Aware Critical Path Selection via Graph Attention Networks

In advanced technology nodes, aging effects like negative and positive bias temperature instability (NBTI and PBTI) become increasingly significant, making timing closure and optimization more challenging. Unfortunately, conventional critical path selection tools used in reliability-aware design flow cannot accurately identify critical paths under different aging conditions. To address this issue, we propose an aging-aware critical path selection flow comprising two parts: critical cell detection and path criticality computation. We employ graph-attention networks (GATs) to predict the critical cells in the aged circuits, and a path criticality computation algorithm that takes into account circuit-level and transistor-level parameters to generate path criticality rank lists. Our experimental results demonstrate that our GAT model outperforms classical machine learning models in detecting critical cells. Additionally, compared with the commercial tool, our aging-aware flow achieves an average accuracy of 99.52%, 98.69%, and 97.20% for top-10%, top-5%, and top-1% path sets respectively, in five industrial designs subjected to different aging conditions and workloads.

Critical Relation Path Aggregation-Based Industrial Control Component Exploitable Vulnerability Reasoning

With the growing discovery of exposed vulnerabilities in the Industrial Control Components (ICCs), identification of the exploitable ones is urgent for Industrial Control System (ICS) administrators to proactively forecast potential threats. However, it is not a trivial task due to the complexity of the multi-source heterogeneous data and the lack of automatic analysis methods. To address these challenges, we propose an exploitability reasoning method based on the ICC-Vulnerability Knowledge Graph (KG) in which relation paths contain abundant potential evidence to support the reasoning. The reasoning task in this work refers to determining whether a specific relation is valid between an attacker entity and a possible exploitable vulnerability entity with the help of a collective of the critical paths. The proposed method consists of three primary building blocks: KG construction, relation path representation, and query relation reasoning. A security-oriented ontology combines exploit modeling, which provides a guideline for the integration of the scattered knowledge while constructing the KG. We emphasize the role of the aggregation of the attention mechanism in representation learning and ultimate reasoning. In order to acquire a high-quality representation, the entity and relation embeddings take advantage of their local structure and related semantics. Some critical paths are assigned corresponding attentive weights and then they are aggregated for the determination of the query relation validity. In particular, similarity calculation is introduced into a critical path selection algorithm, which improves search and reasoning performance. Meanwhile, the proposed algorithm avoids redundant paths between the given pairs of entities. Experimental results show that the proposed method outperforms the state-of-the-art ones in the aspects of embedding quality and query relation reasoning accuracy.

A New Enhanced ARAS Method for Critical Path Selection of Engineering Projects with Interval Type-2 Fuzzy Sets

Appraising the alternative among a set versus conflicting factors is taken into account as an essential issue in real-world decision problems. In this paper, a new multicriteria group decision-making (MCGDM) model is introduced with a fuzzy relative preference relation (FRPR) concept and additive ratio assessment (ARAS) method. FRPR is a useful way to reduce time complexity and to avoid pairwise comparisons. Also, a new method for determining the weights of experts by using an extension of the reference point method is presented and added to this new MCGDM model for an aggregation of the experts’ judgments. Finally, a case study about the selection problem of the engineering project in exploration and sampling projects of lead and zinc mine by decisive criteria are solved to denote the capability of the presented model. Furthermore, to illustrate the various applications of the proposed method in different decision problems, an example of literature is solved.

Selecting Representative Critical Paths for Sensor Placement Provides Early FPGA Aging Information

This article proposes a methodology for critical path selection and delay sensor insertion for aging monitoring in field-programmable gate arrays (FPGAs). The aging information can be used to reconfigure FPGAs to achieve better performance or wear leveling. To filter out the paths aging less aggressively, our methodology decides based on both physical-level parameters [e.g., path delay, process variation, temperature, static stress (duty cycle), and dynamic stress (switching activity) as well as aging-relevant parameters (e.g., fan-out, and endpoint physical location)]. After selection of an optimal set of paths, age sensors, introduced in our earlier work, are placed in a distributed fashion throughout the FPGA area to provide aging information of its various parts as they are being used. Accurate aging models for FPGAs are required to determine the contribution of the above-mentioned parameters in aging. In this article, ASICs’ aging models are adapted for FPGAs through measurement-based fitting approach. The experimental results using various benchmarks reveal that our algorithm selects paths with a minimum error.

Test Pattern Generation and Critical Path Selection in the Presence of Statistical Delays

The statistical delay of a path is traditionally modeled as a Gaussian random variable assuming that the path is always sensitized by a test pattern. Its sensitization in various circuit instances varies among its test patterns and the pattern induced delay is non-Gaussian. It is modeled using probability mass functions (PMFs). This article presents an automatic test pattern generation (ATPG) method, where multiple uncorrelated test patterns per path improve its defect coverage (DC). The impact of the ATPG process is evaluated by comparing to traditional methods. It is also shown that the presented ATPG is useful in selecting critical paths.

Potential Critical Path Selection Based on a Time-Varying Statistical Timing Analysis Framework

Negative bias temperature instability along with the presence of process variations has resulted in time-varying path criticalities. To ensure reliable circuit operation, aging sensors are used at the end of potential critical paths (PCPs) for delay monitoring. Optimization of the number of delay sensors requires accurate computational models for prediction of criticality and selection of PCPs. We identify a path as a PCP if its maximum global criticality over the lifetime exceeds a certain threshold. However, the global criticality of a path could vary nonmonotonically over the lifetime of the device. In this paper, we propose a framework for time-varying statistical static timing analysis (TV-SSTA), wherein the circuit delay is obtained as a collection of time-varying canonicals with breakpoints in time which define the end of validity of one and the start of the next canonical. We show that the global criticality of any path will be maximum either at $t = 0$ or at these breakpoints. Hence, criticality computation and PCP selection need to be done only at these time points, which typically is less than four. The TV-SSTA is integrated with a previously proposed criticality computation technique to identify the PCPs and the results are validated against Monte Carlo simulations.

Solution of fuzzy multi criteria project management problem by Fuzzy programming technique with possibilistic approach

Objective: This study contains a linear and exponential membership function based fuzzy programming technique with possibilistic approach and its application to find the critical path in project network. Methods: It contains four criteria; cost, quality, time and risk of the project activities for project management. For finding the solution of this multi-criteria project management problem in fuzzy programming technique for better decision by Decision Maker (DM) alpha level set concept is utilized. We have provided numerical illustration to demonstrate working of the proposed methodology. Findings: To analyse the performance of the proposed approach, we have compared it with closely related fuzzy group multi-criteria decision making related Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method for the critical path selection. Application: Further, a case study from manufacturing engineering industry is also presented to justify the applicability and potentials of proposed methodology in a better way. Degree of satisfaction is calculated for different values of alpha levels to validate the applicability of this new approach. Keywords: α-level, Critical Path, Fuzzy Programming, Project Management, Possibilistic Approach

FLINT+: A runtime-configurable emulation-based stochastic timing analysis framework

ASICs for Stochastic Computing conditions are designed for higher energy-efficiency or performance by sacrificing computational accuracy due to intentional circuit timing violations. To optimize the stochastic behavior, iterative timing analysis campaigns have to be carried out for a variety of circuit timing corner cases. However, the application of common event-driven logic simulators usually leads to excessive analysis runtimes, increasing design time for hardware developers. In this paper, a gate-level netlist-oriented FPGA-based timing analysis framework is proposed, offering a runtime-configuration mechanism for emulating different timing corner cases in hardware without requiring multiple FPGA bitstreams. Logic gates are instrumented with a quantization-based delay model and a critical path selection algorithm is used to reduce the FPGA resource overhead. For an exemplary design space exploration of stochastic CORDIC units, speed-up factors of up to 48 for 10 ps or 476 for 100 ps timing quantization are achieved while maintaining timing behavior deviations lower than 1.5% or 4% to timing simulations, respectively.

A New Interval Type-2 Fuzzy Decision Method with an Extended Relative Preference Relation and Entropy to Project Critical Path Selection

Considering uncertainty in multi-criteria decision making (MCDM) is an important issue in today's business and management problems. In this article, to use advantages of IT2FSs, a novel interval type-2 fuzzy multi-criteria decision method is presented with an extended entropy and relative preference relation. To tackle vagueness and uncertainty of real-world problems, the IT2FSs are used and applied to a modified MCDM method. Furthermore, an entropy method is developed under an IT2F environment and for obtaining the final weight of each criterion, a relative preference relation is hybridized with an entropy method. Also, the weight of each decision maker (DM) is calculated by a new IT2F-order preference method by means of the relative closeness. Finally, an existing example about the project critical path selection by considering effective criteria, such as time, cost, quality and safety, is adopted from the literature and solved to indicate the capability of introduced method.

Selection of Critical Paths for Reliable Frequency Scaling under BTI-Aging Considering Workload Uncertainty and Process Variations Effects

Conventional clock guardbanding to assure a circuit’s reliable operation under device aging due to NBTI/PBTI and process variations introduce significant performance loss in modern nanometer circuits. Dynamic Frequency Scaling (DFS) is a more efficient technique that allows us to adjust the system clock frequency according to the process condition and aging deterioration of the circuit. At the design phase, the DFS technique requires the identification of the logic paths to be monitored to introduce the required circuitry to monitor their delay. However, critical path identification is a complex problem due to three major challenges: (1) The critical paths of the circuit depend on the stress duty cycle of the devices, which are unknown in advance at design phase; (2) the critical paths of the circuit depend on the process parameters variations, whose impact on delay depend on the spatial correlation due to proximity at the circuit layout; and (3) the critical paths reordering probability may change over time due to aging. This article presents a methodology for efficient selection of the critical paths to be monitored under a DFS framework, addressing the aforementioned challenges. Experimental results on ISCAS 85/89 benchmark circuits show the feasibility of the proposed approach to select a restricted path set while providing reliable aging monitoring.

An Efficient False Path-Aware Heuristic Critical Path Selection Method with High Coverage of the Process Variation Space

In this article, we present a critical path selection method that efficiently finds true (sensitizable) critical paths of a circuit in the presence of process variations. The method, which is based on the viability analysis, tries to select the least number of true critical paths that cover all of circuit critical gates. Critical gates are those that make a path critical with a probability higher than a predefined threshold value. Selecting fewer critical paths leads to less computation time for the algorithm and shorter test time of fabricated chips. For this purpose, an efficient Statistical Static Timing Analysis– (SSTA) based technique is suggested. This technique tries to find circuit-critical gates whose process parameter variations cover a major part of the process space. Improving the process space coverage using fewer paths is achieved by considering both spatial (proximity of gates) and structural (having common gates) correlations in the analysis of choosing the critical paths. In the selection process, paths with low similarities in their characteristics are preferred. In addition, only true paths whose delays affect the maximum delay of the circuit are included. The selected paths can be used in the test process of the fabricated chips to determine if the chip meets its timing requirements. Also, a modified viability analysis that incorporates statistical computations is used in the SSTA. The efficacy of the proposed method is evaluated by comparing its results for combinational and sequential ISCAS benchmarks with those obtained by exhaustive search. Results indicate although, on average, only 4.38% of all the critical paths found by the exhaustive search are selected by the proposed method, the maximum probability of criticality for the paths that are not considered in our method is, on average, less than 4%.

Intuitionistic fuzzy multi-criteria group decision making with an application to critical path selection

In this paper, we develop a new fuzzy multi-criteria group decision making method using triangular intuitionistic fuzzy numbers (TIFNs) for determining critical path in a critical path problem (CPP). The CPP considered here involves both quantitative and qualitative assessments of the decision makers on multiple conflicting criteria. The intuitionistic fuzzy numbers are introduced since they consider both preferences and non-preferences simultaneously and are thus capable of representing qualitatively evaluated information more effectively than fuzzy sets. The proposed method involves fuzzy evaluation based on the extended preference relation of TIFNs using \((\alpha ,\beta )\)-cuts considered for preferences and non-preferences, respectively. The preference intensity function based on the extended preference relation of TIFNs leads to the strength and weakness index scores of the possible paths on given criteria. Furthermore, we define the total performance score of each project path using its strength and weakness index scores. The path that has the highest score is selected as the best alternative in terms of its criticality for the entire project to finish as per the chosen criteria. A numerical illustration is provided to demonstrate working of the proposed methodology.

Non-enumerative Generation of Path Delay Distributions and Its Application to Critical Path Selection

A Monte Carlo-based approach is proposed capable of identifying in a non-enumerative and scalable manner the distributions that describe the delay of every path in a combinational circuit. Furthermore, a scalable approach to select critical paths from a potentially exponential number of path candidates is presented. Paths and their delay distributions are stored in Zero Suppressed Binary Decision Diagrams. Experimental results on some of the largest ISCAS-89 and ITC-99 benchmarks shows that the proposed method is highly scalable and effective.

Early Selection of Critical Paths for Reliable NBTI Aging-Delay Monitoring

Aging effects in advanced technologies produce significant performance degradation as time progresses. In order to guarantee safe operation, aging-delay monitors can be inserted at the output nodes of critical paths (CPs) to allow predictive error detection. However, online monitoring of a large number of CPs that can exist in the state-of-art designs is not feasible. The conventional statistical selection of CPs requires knowledge of the coordinates of each gate in the corresponding layout of the circuit to account for spatial correlation between devices’ process parameters. This paper presents a nonspatial-correlation-dependent methodology to select the CPs for aging-delay monitoring for predictive error detection. Spatial correlation is bounded by a statistical approach maximizing CPs’ coverage. The proposed early selection methodology is validated by comparing the obtained results with those obtained with the availability of spatial correlation information extracted from the circuit layout. The results clearly show that the set of CPs selected with the proposed early selection methodology is in good agreement with the one selected with the availability of layout information. Therefore, our proposed methodology is very attractive to be used in the early design stages, where detailed circuit layout is not available.

A new fuzzy group multi-criteria decision making method with an application to the critical path selection

In this paper, we propose a new fuzzy group multi-criteria decision making method and apply it to determine the critical path in a project network. The criteria used here are time (expected duration), cost, risk, and quality of the project activities that are considered critical in project management. As each criterion has its independent level of importance in the critical path selection, the weights of the project criteria are also considered in the analysis. Considering that the information in terms of various project activities and criteria weights are often incomplete and/or uncertain in real-world situations, the essential information in terms of the criteria and project activities are obtained using triangular fuzzy numbers and/or linguistic variables that are mapped to triangular fuzzy numbers, wherever appropriate. The proposed method involves fuzzy evaluation based on the fuzzy information of the possible project paths on each criterion leading to the strength and weakness index scores of the project paths. We define a measure of criticality termed as the total performance score of each project path obtained using its strength and weakness index scores. The path that has the highest measure of criticality is selected as the critical path. A numerical illustration is provided to demonstrate working of the proposed methodology. Further, a case study from manufacturing engineering industry is also presented to better justify the applicability and potentials of the proposed methodology. A comparison with closely related fuzzy multi-criteria decision methods for the critical path selection is done to analyze the performance of the proposed methodology.

Aging- and Variation-Aware Delay Monitoring Using Representative Critical Path Selection

Process together with runtime variations in temperature and voltage, as well as transistor aging, degrade path delay and may eventually induce circuit failure due to timing variations. Therefore, in-field tracking of path delays is essential, and to respond to this need, several delay sensor designs have been proposed in the literature. However, due to the significant overhead of these sensors and the large number of critical paths in today's IC, it is infeasible to monitor the delay of every critical path in silicon. We present an aging- and variationaware representative path selection technique based on machine learning that allows to measure the delay of a small set of paths and infer the delay of a larger pool of paths that are likely to fail due to delay variations. Simulation results for benchmark circuits highlight the accuracy of the proposed approach for predicting critical-path delay based on the selected representative paths.

Testable Critical Path Selection Considering Process Variation

Critical path selection is very important in delay testing. Critical paths found by conventional static timing analysis (STA) tools are inadequate to represent the real timing of the circuit, since neither the testability of paths nor the statistical variation of cell delays caused by process variation is considered. This paper proposed a novel path selection method considering process variation. The circuit is firstly simplified by eliminating non-critical edges under statistical timing model, and then divided into sub-circuits, while each sub-circuit has only one prime input (PI) and one prime output (PO). Critical paths are selected only in critical sub-circuits. The concept of partially critical edges (PCEs) and completely critical edges (CCEs) are introduced to speed up the path selection procedure. Two path selection strategies are also presented to search for a testable critical path set to cover all the critical edges. The experimental results showed that the proposed circuit division approach is efficient in path number reduction, and PCEs and CCEs play an important role as a guideline during path selection.

Critical Path Selection for Delay Testing Considering Coupling Noise

The objective of delay testing is to detect any defects or variations that manifest into timing failures. In path based delay testing this is done by testing a subset of paths in the circuit that are more likely to fail and hence are critical. Since path delays are vector dependent, the set of critical paths selected depends on the vectors assumed when estimating the path delays. This implies that to find the real critical paths, it is important to consider the effect of dynamic (vector dependent) delay effects such as coupling noise and supply noise during path selection. In this work a methodology to incorporate the effect of coupling noise during path selection is described. For any given path, both logic and timing constraints are extracted and a constrained optimization problem is formulated to estimate the maximum path delay in the presence of coupling noise.

Critical Path Selection for Delay Fault Testing Based Upon a Statistical Timing Model

Critical path selection is an indispensable step for testing of small-size delay defects. Historically, this step relies on the construction of a set of worst-case paths, where the timing lengths of the paths are calculated based upon discrete-valued timing models. The assumption of discrete-valued timing models may become invalid for modeling delay effects in the deep submicron domain, where the effects of timing defects and process variations are often statistical in nature. This paper studies the problem of critical path selection for testing small-size delay defects, assuming that circuit delays are statistical. We provide theoretical analysis to demonstrate that the new path-selection problem consists of two computationally intractable subproblems. Then, we discuss practical heuristics and their performance with respect to each subproblem. Using a statistical defect injection and timing-simulation framework, we present experimental results to support our theoretical analysis.

Critical path selection for performance optimization

The problem of selecting a set of paths to optimize the performance of a combinational circuit is studied, assuming that gate resizing and buffer insertion are the two possible optimizing techniques for reducing the delay of a circuit. The objective of the path selection problem is to select as small as possible a set of paths to ease the optimization processing to guarantee that the delay of the circuit is no longer than a given threshold tau if the delays of all the selected paths are no longer than tau . It is shown that the path selection is different from path sensitization. An input vector-oriented path selection algorithm is proposed. Because it may be infeasible for complex circuits with many primary inputs, a path-oriented algorithm is also developed and implemented. Experimental results on ISCAS85 benchmark circuits show a potentially big improvement for the optimization process.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>