Timing Validation Abstraction Refinement for Real-Time Task Scheduling
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Solution Overview
Problem
Conventional methods for timing property validation in real-time embedded systems face scalability limitations due to the state explosion problem and fail to accurately model parameters like task offset and jitter, leading to inefficiencies in scheduling tasks on processors.
Innovation Solution
A method and system for abstraction refinement-based timing validation using Counter Example Guided Abstraction Refinement (CEGAR) to validate timing properties, involving the construction of a Directed Acyclic Graph (DAG) from task specifications, computation of symbolic variables, and refinement analysis to identify and remove spurious execution traces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional SMT-based formal analysis is used to validate timing properties, then validation accuracy is improved, but scalability deteriorates due to state explosion problem
Solution Approach 1:
The patent segments the timing validation process into multiple phases: initial abstract analysis phase and detailed refinement phase. The state space is divided into abstract representations that can be validated efficiently, with refinement applied only to specific regions where timing constraints need detailed verification. This segmentation allows the system to maintain scalability while preserving validation accuracy for critical timing properties.
Solution Approach 2:
The patent introduces an additional dimension of abstraction levels in the validation process. Instead of working directly with the full state space, the system operates at multiple abstraction levels, transitioning from high-level abstract models to more detailed representations only when necessary. This dimensional approach to abstraction allows efficient validation while maintaining the ability to verify timing properties with required precision.
2Productivity
If closed-form analytical tests are used for timing validation, then computational efficiency is improved, but measurement precision deteriorates due to limited applicability
Solution Approach 1:
The patent applies partial action by using closed-form analytical tests only for the portion of the validation that can be efficiently handled at an abstract level. For remaining timing properties that require higher precision, the system applies refinement analysis selectively. This partial application of analytical tests maintains computational efficiency while achieving required validation accuracy through targeted refinement.
Solution Approach 2:
The patent introduces an intermediary refinement analysis mechanism that bridges the gap between efficient closed-form analytical tests and accurate detailed validation. The refinement analysis acts as a mediator, taking the results from abstract analytical tests and selectively applying detailed analysis only where needed, thus combining the efficiency of analytical methods with the precision of formal verification.
3Measurement precision
If detailed models including task offset and jitter are used, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent applies dynamics by making the model complexity adaptive rather than static. The system starts with simplified models that exclude detailed parameters like task offset and jitter to maintain low complexity. When validation requires higher precision, the system dynamically refines the model to include these parameters only for specific tasks or time periods where they are critical, thus maintaining overall model simplicity while achieving required precision where needed.
Solution Approach 2:
The patent applies local quality by incorporating detailed parameters such as task offset and jitter only in local regions of the model where they are necessary for accurate timing validation. Instead of uniformly complexifying the entire model, the system selectively adds detailed representations only for critical tasks or time intervals, maintaining model simplicity in non-critical areas while achieving high precision where required.
Data Source
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AI summary
The present disclosure provides an abstraction refinement for analyzing timing properties of real-time applications in an efficient, scalable and accurate manner. Conventional methods focus on closed-form analytical tests because of their efficiency and lacks scalability. The present disclosure receives a plurality of task specifications. A time horizon is computed based on the plurality of task specifications. A plurality of time spawned jobs is obtained based on the computed time horizon. Further, a Directed Acyclic Graph (DAG) is constructed for the plurality of time spawned jobs. A plurality of symbolic variables are obtained from the DAG and a plurality of timing constraints are computed. The plurality of constraints and a plurality of timing properties are verified by a verification engine to obtain a set of timing property violated jobs. Here, spurious traces are identified from the execution trace and removed using a plurality of refinement properties.