A Method for Redundancy Assessment and Optimization of Agent Networks Based on Hypothetical Attacks

Abstract

This invention discloses a method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks, comprising the following steps: 1) constructing a multi-agent cluster network meta-model; 2) following object-oriented modeling methods and based on meta-model mapping rules, constructing an executable model; 3) constructing a Bayesian network model and performing real-time calculation of redundancy and task execution probability during the attack process; 4) designing attack scenarios and configuring parameters; 5) verifying the consistency between the evaluation index model and the network executable model based on the attack response boundary mechanism; 6) verifying the traceability of redundancy and task execution probability based on linkage simulation; 7) executing a hypothetical attack and evaluating redundancy; 8) generating an optimization scheme based on the evaluation results. This invention proposes an evaluation and optimization method based on the consistency between the evaluation index model and the network executable model by achieving consistency in the structure, behavior, and index traceability of the two types of models.

Description

Technical Field

[0001] This invention relates to computer technology, and more particularly to a method for evaluating and optimizing the redundancy of intelligent agent networks based on hypothetical attacks. Background Technology

[0002] Existing methods for assessing the reliability of multi-agent cluster networks have gradually established a standardized process from network topology analysis to redundancy index output, providing an overall framework for the deployment and operation of multi-agent clusters in complex environments. Among these, attack scenario simulation and evaluation model parameter setting are core steps that directly affect the subsequent performance of the cluster's resilience system and play a decisive role in the rationality of the assessment results.

[0003] Currently, redundancy can be defined and quantified through global network attributes, providing a unified metric for resilience assessment. The established assessment model uses node removal to uncover the correlation between redundancy and node importance, demonstrating its effectiveness in prioritizing nodes in large-scale networks and providing a basis for network protection decisions under cost constraints. In terms of technical methods, current mainstream approaches can be divided into three categories: First, static parameter quantification methods, such as calculating redundancy through topological features like node degree and the number of shortest paths, or drawing on machine learning models to construct a redundancy resource allocation model based on the load-capacity linear relationship; second, structural redundancy identification methods, using techniques such as tensor decomposition and minimum redundancy maximum correlation to identify recurring attributes and redundant subgraphs in graph models, optimizing the network topology; and third, dynamic optimization attempts, such as the DRC model, which adjusts node redundancy capacity to address cascading failures, but still focuses on improving load redistribution strategies.

[0004] However, in practical applications, existing multi-agent cluster networking redundancy assessment and optimization technologies still have significant problems in complex environments. They are unable to meet the actual needs of accurate network reliability assessment and scientific prediction of task execution risks, and there is a gap between them and the requirements for ensuring the stable operation of multi-agent clusters. Specifically, the problems are as follows: First, the lack of mapping of assessment elements and the single-dimensionality result in a one-sided characterization of the resilience of multi-agent cluster networks. Currently, the assessment of cluster network redundancy relies heavily on expert subjective judgment for key parameters, failing to construct a quantitative modeling and analysis system based on the unique communication and cooperation characteristics of multi-agent clusters. Furthermore, the assessment process lacks a complete mapping relationship between "attack scenarios - redundancy attributes - resilience," and the construction logic of key impact chains is unclear, failing to comprehensively reflect the cluster's anti-interference capabilities under multiple scenarios. Ultimately, this leads to one-sided redundancy assessment results, making it difficult to support a comprehensive judgment of network resilience.

[0005] Second, the misalignment of model behavioral logic and the disconnect of the verification process lead to insufficient accuracy in task execution probability prediction and deviations from actual operation. Although multi-agent cluster network evaluation often uses network simulation models to verify results, existing redundancy assessment models and network simulation models are mostly built independently without establishing a dynamic consistency association. The two have problems with incomplete mapping and semantic inconsistency in core behavioral logic, and the entire process lacks a logical closed loop, making it impossible to accurately simulate the linkage relationship of actual tasks. As a result, the predicted task execution probability results deviate significantly from the actual operation, and the accuracy is insufficient to meet the requirements of risk prediction.

[0006] Third, incomplete indicator support and insufficient scenario adaptability result in models that cannot cover complex and ever-changing attack scenarios, limiting their adaptability. In existing technologies, redundancy assessment models and network executable models only establish limited mapping relationships on some basic links, which is insufficient to support key indicators for complex attack scenarios. Furthermore, the coverage of core elements such as node state parameters and attack and defense behavior logic is low, making it impossible to adapt to the characteristics of complex and ever-changing attack scenarios. Ultimately, this limits the model's scenario adaptability and makes it difficult to provide scientific assessment support for the stability of cluster operation under various attack scenarios.

[0007] In summary, current technologies lack a method to verify the consistency between the redundancy assessment model and the network executable model, and to trace, verify, and optimize task execution capability indicators based on this consistency relationship. To address these issues, a consistency-driven assessment and verification mechanism is urgently needed. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method for evaluating and optimizing the redundancy of intelligent agent networks based on hypothetical attacks, addressing the deficiencies in the existing technology.

[0009] The technical solution adopted by this invention to solve its technical problem is: a method for evaluating and optimizing the redundancy of intelligent agent networks based on hypothetical attacks, comprising the following steps: 1) Construct a multi-agent cluster networking element model; Based on the characteristics of multi-agent system architecture, the elements of the meta-model are defined; This includes node types, link types, attack scenario types, and indicator types, clearly defining the attributes and parameters of each type of element; 2) Following object-oriented modeling methods and based on meta-model mapping rules, construct an executable model; include: Agent nodes are mapped to node classes in the executable model, where the connectivity importance of nodes is... Mapped to class attribute variables; The communication link is mapped to the link method, and the link's transmission quality coefficient is... Mapped to the output parameters of the method; Attack rules are mapped to the flow control logic within a method, and the attack strength coefficient is... As a condition for logical judgment; Redundancy indexes are mapped to class attribute variables; 3) Construct a Bayesian network model to perform real-time calculations of redundancy and task execution probability during the attack process; The design uses a directed acyclic graph with node status, link quality, and attack strength as parent nodes, and redundancy and task execution probability as child nodes. 4) Design attack scenarios and configure parameters. 4.1) Construction of a hierarchical hypothetical attack scenario system; 4.2) The parameters of the meta-model, executable model, and Bayesian network model are unified from three dimensions: structural consistency, parameter mapping verification, and attack rule alignment. 5) Consistency verification between the evaluation index model based on the attack response demarcation point mechanism and the network executable model; the evaluation index model is a redundancy evaluation model, and the index calculation is realized based on Bayesian network probabilistic inference. 6) Redundancy and task execution probability can be traced and verified based on linkage simulation; 7) Perform a hypothetical attack and conduct a redundancy assessment; Collect node status, link quality, and redundancy data; 8) Generate an optimized solution based on the evaluation results.

[0010] According to the above scheme, in step 1), the attributes and parameters of various elements are as follows: Node classes: Classified by function into sensing nodes, decision nodes, and execution nodes, recording node type, hardware parameters, and initial resource quantity attributes; Link Classes: Includes wireless communication links and wired transmission links; defines the upper limit of link bandwidth. Maximum delay Basic bit error rate parameter; Attack scenarios include: attack types: single-point attack, area interference, coordinated attack; attack parameters: attack strength coefficient. Attack duration; Metrics: Including redundancy metrics such as link redundancy entropy. Task execution metric: Task execution probability Data transmission success rate .

[0011] According to the above scheme, in step 2), in the element mapping relationship, the agent node is mapped to the node class in the executable model. The connectivity importance of nodes Mapped to class attribute variables, , In the formula For nodes arrive The total number of shortest paths, For the nodes The number of shortest paths, This represents the total number of nodes.

[0012] According to the above scheme, in step 2), the element mapping relationship includes a communication link mapped to a link method, and the link's transmission quality coefficient. Mapped to the output parameters of the method. , in The weighting coefficients and , This is the actual bandwidth. For maximum bandwidth, For transmission delay, For the maximum allowable delay, This refers to the bit error rate.

[0013] According to the above scheme, in step 2), the attack rules in the element mapping relationship are mapped to the flow control logic inside the method, and the attack strength coefficient is... As a condition for logical judgment. , in For the first In the class of attacks, the first The actual value of the parameter, For the first The maximum threshold of the parameter, For the first The weight of the item parameter, The number of attack parameters, with a range of values. .

[0014] According to the above scheme, step 5) specifically involves the following: decomposing the evaluation index model and the network executable model into behavioral processes, identifying key logical stage nodes, including the attack initialization stage, the node / link state change stage, the redundancy calculation stage, and the task execution judgment stage. Establish the logical correspondence between the two models at the corresponding stages and construct the behavioral interaction interface; The evaluation index model drives the executable model to perform linkage simulation, and observes whether the behavior paths and data transmission of both parties are consistent at each stage.

[0015] According to the above scheme, step 6) specifically includes the following: Define the target value for redundancy index Boundary values , With reference input parameters, including the number of nodes Link type Attack strength range ; By using model-driven simulations, scenarios under different attack intensities are run to evaluate the completion time of critical tasks. Resource consumption rate , in For the first The actual consumption of such resources For the first The maximum available quantity of such resources, For the first The weight of class resources, Total number of resource types; By comparing the simulation results with the preset target values, we can determine the rationality of the current target value setting.

[0016] According to the above scheme, in step 6), Pareto optimality-based network optimization is adopted, with the objective function being to minimize resource consumption rate and maximize task execution probability.

[0017] The beneficial effects of this invention are: 1. This invention proposes a method for verifying the consistency of evaluation index models and network executable model elements based on meta-model driven methods, a method for verifying the consistency of evaluation index models and network executable model behaviors based on attack response demarcation point mechanisms, and a method for verifying redundancy and task execution probability based on linkage simulation. These methods effectively solve prominent problems in the current quantitative generation process of multi-agent cluster evaluation, such as missing model element mapping, difficulty in aligning behavioral logic, and lack of support for index verification. They provide a traceable verification technology system for redundancy and task execution probability analysis. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0020] like Figure 1 As shown, a method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks includes the following steps: 1) Construct a multi-agent cluster networking element model; Based on the characteristics of multi-agent system architecture and the need for redundancy assessment, the elements of the meta-model are defined. It includes node categories, link categories, attack scenario categories, and indicator categories, clearly defining the attributes and parameters of each concept (such as node connectivity importance, link transmission quality coefficient, and attack strength coefficient), and establishing semantic relationships through meta-model tools to form a visual graph; Among them, the node class is divided into sensing nodes, decision nodes, and execution nodes according to their functions, and records the node type, hardware parameters, and initial resource quantity attributes. Link Classes: Includes wireless communication links and wired transmission links; defines the upper limit of link bandwidth. Maximum delay Basic bit error rate parameter; Attack scenarios include: attack types: single-point attack, area interference, coordinated attack; attack parameters: attack strength coefficient. Attack duration; Metrics: Including redundancy metrics such as link redundancy entropy. Task execution metric: Task execution probability Data transmission success rate ; 2) Following object-oriented modeling methods and based on meta-model mapping rules, construct an executable model; include: Agent nodes are mapped to node classes in the executable model, where the connectivity importance of nodes is... Mapped to class attribute variables; The communication link is mapped to the link method, and the link's transmission quality coefficient is... Mapped to the output parameters of the method; Attack rules are mapped to the flow control logic within a method, and the attack strength coefficient is... As a condition for logical judgment; Redundancy indexes are mapped to class attribute variables; Element mapping relationship: Agent nodes are mapped to node classes in the executable model, where the connectivity importance of nodes is... Mapped to class attribute variables, In the formula For nodes arrive The total number of shortest paths, For the nodes The number of shortest paths, This represents the total number of nodes; ensure that node descriptions are consistent. The communication link is mapped to the link method, and the link's transmission quality coefficient is... Mapped to the output parameters of the method. ,in The weighting coefficients and , This is the actual bandwidth. For maximum bandwidth, For transmission delay, For the maximum allowable delay, The bit error rate, i.e., the transmission capacity of the link, is expressed by a method. Attack rules are mapped to the flow control logic within a method, and the attack strength coefficient is... As a condition for logical judgment. ,in For the first In the class of attacks, the first The actual value of the parameter, For the first The maximum threshold of the parameter, For the first Weights of the item parameters , The number of attack parameters, with a range of values. ; Redundancy metrics are mapped to class attribute variables, such as link redundancy entropy. As the core variable, ,in For the first The proportion of similar links in the set of effective links. Total number of link types; Task data flow is mapped to data interaction flow between models, and the data transmission success rate is... As a quality indicator of interactive flow ,in For the first Bit error rate of each data packet, For the first Importance weights of each data group ( ), Total number of data groups; Capability associations indicate that a node class possesses the ability to execute a certain task method, and the probability of task execution. (in, = F ( ), To enable each node to perform tasks. F (*) represents the interaction function, which serves as a capability metric and is associated with node remaining resources and link quality. 3) Bayesian network model construction; The network structure design uses a directed acyclic graph with node status, link quality, and attack strength as parent nodes, and redundancy and task execution probability as child nodes. Real-time calculation of redundancy and task execution probability under a given attack scenario using a Bayesian network model; Parameter learning: Training a prior probability table using historical attack data, such as the link transmission quality coefficient when the node is in normal working condition. Conditional probability distributions falling into different intervals Establish a quantitative correlation between the attack strength coefficient and the node failure state, i.e., given the attack strength... The conditional probability of a time node entering a failure state ; Inference engine integration: The junctiontree algorithm is used to implement probabilistic inference, supporting real-time calculation of redundancy and task execution probability under a given attack scenario.

[0021] The Bayesian network model works in conjunction with the network executable model to receive dynamic updates of node status and link quality in real time, and quickly update the probabilistic inference results to achieve real-time quantitative evaluation of redundancy and task execution probability during the attack process. 4) Design attack scenarios and configure parameters. 4.1) Construction of a hierarchical hypothetical attack scenario system; The scenarios are divided into three levels based on the attack intensity gradient: Level 1 scenario (light attack): Simulate single-point device interference; attack parameters are set to the duration of single-node communication interference. Minutes, Bit Error Rate Increase ; Level 2 scenario (moderate attack): Simulated area link damage, attack range coverage With adjacent nodes, bandwidth decreases to The latency increased to ; Level 3 scenario (severe attack): Simulated cluster coordination failure, attacks causing core decision-making nodes to degrade, link redundancy entropy The sudden drop threshold is set to .

[0022] Each scenario is configured with a corresponding parameter template, which includes key elements such as attack triggering conditions, scope of impact, and duration.

[0023] 4.2) The parameters of the meta-model, executable model, and Bayesian network model are unified from three dimensions: structural consistency, parameter mapping verification, and attack rule alignment. Model consistency parameter calibration Align the evaluation metric model with the parameters of the executable network model using meta-model mapping rules: Structural consistency check: Compare the attribute coverage of metamodel node classes with executable model node classes to ensure connectivity importance. Damage resistance coefficient All core parameters are present; Parameter mapping verification: Verification of link transmission quality coefficients Data transmission success rate Cross-model calculations and comparisons of indicators such as [list of indicators] must be performed, and the error must be controlled within [a certain range]. within; Attack rule alignment: Ensuring attack strength in Bayesian networks The probability distribution is consistent with the trigger threshold of the attack response logic in the executable model.

[0024] 5) Consistency verification between the evaluation index model based on the attack response demarcation point mechanism and the network executable model; The simulation process is broken down into four stages: attack initialization, state change, redundancy calculation, and task judgment, so as to achieve synchronization of the behavior of the evaluation index model and the executable model; the evaluation index model is a redundancy evaluation model. The evaluation index model and network executable model are decomposed into behavioral processes to identify key logical stage nodes. The logical stages include the attack initialization stage, the node / link state change stage, the redundancy calculation stage, and the task execution judgment stage. Establish the logical correspondence between the two models at the corresponding stages and construct the behavioral interaction interface; The behavioral interactions at each stage are as follows: Attack initialization phase: The evaluation index model sends attack scenario parameters to the executable model. (Attack target), the executable model returns an initial network topology snapshot; State transition phase: The executable model updates the node state according to the attack rules. (through functional normality rate) (Judgment), and real-time uploading of status change logs; Redundancy calculation phase: The evaluation model calculates the link redundancy entropy. The executable model synchronously calculates the actual redundancy level. ,when Time-triggered parameter correction; Task determination phase: Both parties calculate the probability of task execution. If the deviation exceeds the threshold, the conditional probability table of the Bayesian network or the node resource allocation strategy will be adjusted.

[0025] The evaluation index model drives the executable model to perform linked simulation, observing whether the behavioral paths and data transmission between the two parties are consistent at each stage: If the behavioral paths are consistent and the data matches, then the redundancy index of the evaluation model should be considered. The actual redundancy level fed back by the executable model satisfy And the task execution probability deviation ( The allowable error threshold is usually set to [value missing]. If the behavior logic remains consistent, then the boundary point rule is returned for node adjustment and correction, and the attack strength coefficient is adjusted accordingly. or node damage resistance coefficient ( Range of values (The larger the value, the stronger the damage resistance.)

[0026] 6) Redundancy and task execution probability can be traced and verified based on linkage simulation; The setting and verification of existing technology evaluation indicators lack an objective closed loop. Current redundancy level classifications and task execution probabilities rely heavily on past expert experience, lacking a quantitative derivation process based on actual network operation data. Even when simulation methods are used for verification, the lack of a clear correlation between the simulation model and the evaluation indicator model makes it impossible to trace the source and logic of the indicators, significantly reducing the credibility of the verification results.

[0027] Based on the multi-agent cluster functional requirements model and network performance metric matrix, the target value of the redundancy index is clearly defined. Boundary values , Compared with reference input parameters (such as the number of nodes) Link type Attack strength range ); By using model-linked simulations, scenarios under different attack intensities are driven to evaluate the completion time of critical tasks. Resource consumption rate ,in For the first The actual consumption of such resources For the first The maximum available quantity of such resources, For the first Weight of class resources ( ), Output indicators such as the total number of resource types; compare the simulation results with the preset target values, if... If the simulation result of the task execution probability is greater than or equal to the target value, then the current target value is considered reasonable; if it deviates significantly from the target value, then the node damage resistance coefficient is adjusted. Or link redundancy configuration; 7) Perform a three-level attack scenario simulation and conduct a redundancy assessment; Collect data such as node status, link quality, and redundancy; Analysis of model consistency: consistency between node failure sequence and redundancy recovery speed; Verify the correlation of key indicators: the decisive impact of data transmission success rate on task execution probability.

[0028] 8) Generate an optimized solution based on the evaluation results.

[0029] Network optimization based on Pareto optimality; Multi-objective modeling: based on resource consumption rate Minimize and task execution probability Maximize the objective function; Optimal solution finding: The NSGA-II algorithm is used to find the Pareto optimal solution set and select feasible solutions such as node hardening schemes and link redundancy configurations. Parameter iteration: Input the optimal solution parameters into the Bayesian network, re-infer the risk probability under the attack scenario, and verify the anti-attack effect of the solution.

[0030] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. An agent networking redundancy evaluation and optimization method based on hypothetical attack, characterized in that, Includes the following steps: 1) Construct a multi-agent cluster networking element model; Based on the characteristics of multi-agent system architecture, the elements of the meta-model are defined; This includes node types, link types, attack scenario types, and indicator types, clearly defining the attributes and parameters of each type of element; 2) Following object-oriented modeling methods and based on meta-model mapping rules, construct an executable model; include: Agent nodes are mapped to node classes in the executable model, where the connectivity importance of nodes is... Mapped to class attribute variables; The communication link is mapped to the link method, and the link's transmission quality coefficient is... Mapped to the output parameters of the method; Attack rules are mapped to the flow control logic within a method, and the attack strength coefficient is... As a condition for logical judgment; Redundancy indexes are mapped to class attribute variables; 3) Construct a Bayesian network model to perform real-time calculations of redundancy and task execution probability during the attack process; The design uses a directed acyclic graph with node status, link quality, and attack strength as parent nodes, and redundancy and task execution probability as child nodes. 4) Design attack scenarios and configure parameters; 4.1) Construction of a hierarchical hypothetical attack scenario system; 4.2) The parameters of the meta-model, executable model, and Bayesian network model are unified from three dimensions: structural consistency, parameter mapping verification, and attack rule alignment. 5) Consistency verification between the evaluation index model based on the attack response demarcation point mechanism and the network executable model; the evaluation index model is a redundancy evaluation model, and the index calculation is realized based on Bayesian network probabilistic inference. 6) The redundancy and task execution probability indicators based on linkage simulation can be traced and verified; 7) Perform a hypothetical attack and conduct a redundancy assessment; Collect node status, link quality, and redundancy data; 8) Based on the evaluation results, generate an optimization plan and perform optimization.

2. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 1), the attributes and parameters of various elements are as follows: Node classes: Classified by function into sensing nodes, decision nodes, and execution nodes, recording node type, hardware parameters, and initial resource quantity attributes; Link Classes: Includes wireless communication links and wired transmission links; defines the upper limit of link bandwidth. Maximum delay Basic bit error rate parameter; Attack scenarios include attack types: single-point attack, area interference, and coordinated attack. Attack parameters: Attack strength coefficient Attack duration; Metrics: Including redundancy metrics such as link redundancy entropy. Task execution metric: Task execution probability Data transmission success rate .

3. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 2), the agent node is mapped to a node class in the executable model within the element mapping relationship. The connectivity importance of nodes Mapped to class attribute variables, ， In the formula For nodes arrive The total number of shortest paths, For the nodes The number of shortest paths, This represents the total number of nodes.

4. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 2), the element mapping relationship includes a communication link mapped to a link method and a link transmission quality coefficient. Mapped to the output parameters of the method. , in The weighting coefficients and , This is the actual bandwidth. For maximum bandwidth, For transmission delay, For the maximum allowable delay, This refers to the bit error rate.

5. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 2), the attack rules in the element mapping relationship are mapped to the flow control logic inside the method, and the attack strength coefficient is... As a condition for logical judgment. , in For the first In the class of attacks, the first The actual value of the parameter, For the first The maximum threshold of the parameter, For the first The weight of the item parameter, The number of attack parameters, with a range of values. .

6. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 5), the specific steps are as follows: decompose the evaluation index model and network executable model into behavioral processes, identify key logical stage nodes, and the logical stages include the attack initialization stage, the node / link state change stage, the redundancy calculation stage, and the task execution judgment stage. Establish the logical correspondence between the two models at the corresponding stages and construct the behavioral interaction interface; The evaluation index model drives the executable model to perform linkage simulation, and observes whether the behavior paths and data transmission of both parties are consistent at each stage.

7. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 6), the specific details are as follows: Define the target value for redundancy index Boundary values , With reference input parameters, including the number of nodes Link type Attack strength range ; By using model-driven simulations, scenarios under different attack intensities are run to evaluate the completion time of critical tasks. Resource consumption rate , in For the first The actual consumption of such resources For the first The maximum available quantity of such resources, For the first Weight of class resources Total number of resource types; By comparing the simulation results with the preset target values, we can determine the rationality of the current target value setting.

8. The method for evaluating and optimizing the redundancy of agent networks based on hypothetical attacks according to claim 1, characterized in that, In step 6), Pareto optimality-based network optimization is adopted, with the objective function being to minimize resource consumption rate and maximize task execution probability.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 8.

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