Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

A BSP Algorithm for the State Space Construction of Security Protocols

International audienceThis paper presents a Bulk-Synchronous Parallel (BSP) algorithm to compute the discrete state space of structured models of security protocols. The BSP model of parallelism avoids concurrency related problems (mainly deadlocks and non-determinism) and allows us to design an efficient algorithm that is at the same time simple to express. A prototype implementation has been developed, allowing to run benchmarks showing the benefits of our algorithm

Distributed Saturation

The Saturation algorithm for symbolic state-space generation, has been a recent break-through in the exhaustive veri cation of complex systems, in particular globally-asyn- chronous/locally-synchronous systems. The algorithm uses a very compact Multiway Decision Diagram (MDD) encoding for states and the fastest symbolic exploration algo- rithm to date. The distributed version of Saturation uses the overall memory available on a network of workstations (NOW) to efficiently spread the memory load during the highly irregular exploration. A crucial factor in limiting the memory consumption during the symbolic state-space generation is the ability to perform garbage collection to free up the memory occupied by dead nodes. However, garbage collection over a NOW requires a nontrivial communication overhead. In addition, operation cache policies become critical while analyzing large-scale systems using the symbolic approach. In this technical report, we develop a garbage collection scheme and several operation cache policies to help on solving extremely complex systems. Experiments show that our schemes improve the performance of the original distributed implementation, SmArTNow, in terms of time and memory efficiency

Algorithms for Verification of Analog and Mixed-Signal Integrated Circuits

Over the past few decades, the tremendous growth in the complexity of analog and mixed-signal (AMS) systems has posed great challenges to AMS verification, resulting in a rapidly growing verification gap. Existing formal methods provide appealing completeness and reliability, yet they suffer from their limited efficiency and scalability. Data oriented machine learning based methods offer efficient and scalable solutions but do not guarantee completeness or full coverage. Additionally, the trend towards shorter time to market for AMS chips urges the development of efficient verification algorithms to accelerate with the joint design and testing phases. This dissertation envisions a hierarchical and hybrid AMS verification framework by consolidating assorted algorithms to embrace efficiency, scalability and completeness in a statistical sense. Leveraging diverse advantages from various verification techniques, this dissertation develops algorithms in different categories. In the context of formal methods, this dissertation proposes a generic and comprehensive model abstraction paradigm to model AMS content with a unifying analog representation. Moreover, an algorithm is proposed to parallelize reachability analysis by decomposing AMS systems into subsystems with lower complexity, and dividing the circuit's reachable state space exploration, which is formulated as a satisfiability problem, into subproblems with a reduced number of constraints. The proposed modeling method and the hierarchical parallelization enhance the efficiency and scalability of reachability analysis for AMS verification. On the subject of learning based method, the dissertation proposes to convert the verification problem into a binary classification problem solved using support vector machine (SVM) based learning algorithms. To reduce the need of simulations for training sample collection, an active learning strategy based on probabilistic version space reduction is proposed to perform adaptive sampling. An expansion of the active learning strategy for the purpose of conservative prediction is leveraged to minimize the occurrence of false negatives. Moreover, another learning based method is proposed to characterize AMS systems with a sparse Bayesian learning regression model. An implicit feature weighting mechanism based on the kernel method is embedded in the Bayesian learning model for concurrent quantification of influence of circuit parameters on the targeted specification, which can be efficiently solved in an iterative method similar to the expectation maximization (EM) algorithm. Besides, the achieved sparse parameter weighting offers favorable assistance to design analysis and test optimization

Rapid Recovery for Systems with Scarce Faults

Our goal is to achieve a high degree of fault tolerance through the control of a safety critical systems. This reduces to solving a game between a malicious environment that injects failures and a controller who tries to establish a correct behavior. We suggest a new control objective for such systems that offers a better balance between complexity and precision: we seek systems that are k-resilient. In order to be k-resilient, a system needs to be able to rapidly recover from a small number, up to k, of local faults infinitely many times, provided that blocks of up to k faults are separated by short recovery periods in which no fault occurs. k-resilience is a simple but powerful abstraction from the precise distribution of local faults, but much more refined than the traditional objective to maximize the number of local faults. We argue why we believe this to be the right level of abstraction for safety critical systems when local faults are few and far between. We show that the computational complexity of constructing optimal control with respect to resilience is low and demonstrate the feasibility through an implementation and experimental results.Comment: In Proceedings GandALF 2012, arXiv:1210.202

Balancing Static Islands in Dynamically Scheduled Circuits using Continuous Petri Nets

High-level synthesis (HLS) tools automatically transform a high-level program, for example in C/C++, into a low-level hardware description. A key challenge in HLS is scheduling, i.e. determining the start time of all the operations in the untimed program. A major shortcoming of existing approaches to scheduling – whether they are static (start times determined at compile-time), dynamic (start times determined at run-time), or a hybrid of both – is that the static analysis cannot efficiently explore the run-time hardware behaviours. Existing approaches either assume the timing behaviour in extreme cases, which can cause sub-optimal performance or larger area, or use simulation-based approaches, which take a long time to explore enough program traces. In this article, we propose an efficient approach using probabilistic analysis for HLS tools to efficiently explore the timing behaviour of scheduled hardware. We capture the performance of the hardware using Timed Continous Petri nets with immediate transitions, allowing us to leverage efficient Petri net analysis tools for making HLS decisions. We demonstrate the utility of our approach by using it to automatically estimate the hardware throughput for balancing the throughput for statically scheduled components (also known as static islands) computing in a dynamically scheduled circuit. Over a set of benchmarks, we show that our approach on average incurs a 2% overhead in area-delay product compared to optimal designs by exhaustive search

Balancing static islands in dynamically scheduled circuits using continuous petri nets

High-level synthesis (HLS) tools automatically transform a high-level program, for example in C/C++, into a low-level hardware description. A key challenge in HLS is scheduling, i.e. determining the start time of all the operations in the untimed program. A major shortcoming of existing approaches to scheduling – whether they are static (start times determined at compile-time), dynamic (start times determined at run-time), or a hybrid of both – is that the static analysis cannot efficiently explore the run-time hardware behaviours. Existing approaches either assume the timing behaviour in extreme cases, which can cause sub-optimal performance or larger area, or use simulation-based approaches, which take a long time to explore enough program traces. In this article, we propose an efficient approach using probabilistic analysis for HLS tools to efficiently explore the timing behaviour of scheduled hardware. We capture the performance of the hardware using Timed Continous Petri nets with immediate transitions, allowing us to leverage efficient Petri net analysis tools for making HLS decisions. We demonstrate the utility of our approach by using it to automatically estimate the hardware throughput for balancing the throughput for statically scheduled components (also known as static islands) computing in a dynamically scheduled circuit. Over a set of benchmarks, we show that our approach on average incurs a 2% overhead in area-delay product compared to optimal designs by exhaustive search