A Data Driven Approach for Algebraic Loop Invariants

Sharma, Rahul; Gupta, Saurabh; Hariharan, Bharath; Aiken, Alex; Liang, Percy; Nori, Aditya V.

doi:10.1007/978-3-642-37036-6_31

Cited by 114 publications

(89 citation statements)

References 26 publications

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“…But the classifier is not guaranteed to be an invariant. To obtain soundness, we augment our learning algorithm with a theorem prover using a standard guessand-check loop [55,54]. We sample, perform learning, and propose a candidate invariant using the set cover approach for learning geometric concepts as described in Section 3.2 (the guess step).…”

Section: Recovering Soundnessmentioning

confidence: 99%

“…When we applied guess-and-check in our previous work [55,54] to infer relevant predicates for verification, we checked for only two out of the three constraints listed above (Section 6). Hence, these predicates did not prove any program property and moreover they were of limited expressiveness (no disjunctions among other restrictions).…”

Section: The Candidate Invariant Is Inductive {I ∧ E}s{i}mentioning

confidence: 99%

“…In addition to limiting the expressiveness to just conjunction of polynomial inequalities, this step is computationally very expensive. In a related work, we ran [48] in a guess-and-check loop to obtain an algorithm [54], with soundness and termination guarantees, for generating polynomial equalities as invariants. A termination proof was possible as [54] can return the trivial invariant true: it is not required to find invariants strong enough to prove some property of interest.…”

Section: Comparison With Tools For Non-linear Invariantsmentioning

confidence: 99%

“…In a related work, we ran [48] in a guess-and-check loop to obtain an algorithm [54], with soundness and termination guarantees, for generating polynomial equalities as invariants. A termination proof was possible as [54] can return the trivial invariant true: it is not required to find invariants strong enough to prove some property of interest. This technique can handle only the benchmarks that require zero bad states in Table 1, whereas our current technique can handle all the benchmarks of [54].…”

Section: Comparison With Tools For Non-linear Invariantsmentioning

confidence: 99%

“…-We augment our learning algorithms with a theorem prover to obtain a sound procedure for computing invariants. This idea of combining procedures for generating likely invariants with verification engines has been previously explored in [49,55,54] (see Section 6). We evaluate the performance of this procedure on challenging benchmarks for invariant generation from the literature.…”

Section: Introductionmentioning

confidence: 99%

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Verification as Learning Geometric Concepts

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Abstract. We formalize the problem of program verification as a learning problem, showing that invariants in program verification can be regarded as geometric concepts in machine learning. Safety properties define bad states: states a program should not reach. Program verification explains why a program's set of reachable states is disjoint from the set of bad states. In Hoare Logic, these explanations are predicates that form inductive assertions. Using samples for reachable and bad states and by applying well known machine learning algorithms for classification, we are able to generate inductive assertions. By relaxing the search for an exact proof to classifiers, we obtain complexity theoretic improvements. Further, we extend the learning algorithm to obtain a sound procedure that can generate proofs containing invariants that are arbitrary boolean combinations of polynomial inequalities. We have evaluated our approach on a number of challenging benchmarks and the results are promising.

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Section: Recovering Soundnessmentioning

confidence: 99%

Section: The Candidate Invariant Is Inductive {I ∧ E}s{i}mentioning

confidence: 99%

Section: Comparison With Tools For Non-linear Invariantsmentioning

confidence: 99%

Section: Comparison With Tools For Non-linear Invariantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ResAna: a resource analysis toolset for (real‐time) JAVA

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Shkaravska

et al. 2013

Concurrency and Computation

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SUMMARYFor real-time and embedded systems, limiting the consumption of time and memory resources is often an important part of the requirements. Being able to predict bounds on the consumption of such resources during the development process of the code can be of great value. In this paper, we focus mainly on memory-related bounds. Recent research results have advanced the state of the art of resource consumption analysis. In this paper, we present a toolset that makes it possible to apply these research results in practice for (real-time) systems enabling JAVA developers to analyse symbolic loop bounds, symbolic bounds on heap size and both symbolic and numeric bounds on stack size. We describe which theoretical additions were needed in order to achieve this. We give an overview of the capabilities of the RESANA (Radboud University Nijmegen, The Netherlands) toolset that is the result of this effort. The toolset can not only perform generally applicable analyses, but it also contains a part of the analysis that is dedicated to the developers' (real-time) virtual machine, such that the results apply directly to the actual development environment that is used in practice.

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Neural State Classification for Hybrid Systems

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Zhang

et al. 2018

Automated Technology for Verification and Analysis

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We introduce the State Classification Problem (SCP) for hybrid systems, and present Neural State Classification (NSC) as an efficient solution technique. SCP generalizes the model checking problem as it entails classifying each state s of a hybrid automaton as either positive or negative, depending on whether or not s satisfies a given time-bounded reachability specification. This is an interesting problem in its own right, which NSC solves using machine-learning techniques, Deep Neural Networks in particular. State classifiers produced by NSC tend to be very efficient (run in constant time and space), but may be subject to classification errors. To quantify and mitigate such errors, our approach comprises: i) techniques for certifying, with statistical guarantees, that an NSC classifier meets given accuracy levels; ii) tuning techniques, including a novel technique based on adversarial sampling, that can virtually eliminate false negatives (positive states classified as negative), thereby making the classifier more conservative. We have applied NSC to six nonlinear hybrid system benchmarks, achieving an accuracy of 99.25% to 99.98%, and a false-negative rate of 0.0033 to 0, which we further reduced to 0.0015 to 0 after tuning the classifier. We believe that this level of accuracy is acceptable in many practical applications, and that these results demonstrate the promise of the NSC approach. arXiv:1807.09901v1 [cs.LG] 26 Jul 2018We call such a function a state classifier. SCP generalizes the model checking problem. Model checking, in the context of SCP, is simply the problem of determining whether there exists a positive state in the set of initial states. Its intent is not to classify all states in S.Classifying the states of a complex system is an interesting problem in its own right. State classification is also useful in at least two other contexts. First, due to random disturbances, a hybrid system may restart in a random state outside the initial region, and we may wish to check the system's safety from that state. Secondly, a classifier can be used for online model checking [26], where in the process of monitoring a system's behavior, one would like to determine, in real-time, the fate of the system going forward from the current (non-initial) state.This paper shows how deep neural networks (DNNs) can be used for state classification, an approach we refer to as Neural State Classification (NSC). An NSC classifier is subject to false positives (FPs) -a state s is deemed positive when it is actually negative, and, more importantly, false negatives (FNs)s is deemed negative when it is actually positive.A well-trained NSC classifier offers high accuracy, runs in constant time (approximately 1 millisecond, in our experiments), and takes constant space (e.g., a DNN with l hidden layers and n neurons only requires functions of dimension l · n for its encoding). This makes NSC classifiers very appealing for applications such as online model checking, a type of analysis subject to strict time and space constraints...

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A Data Driven Approach for Algebraic Loop Invariants

Cited by 114 publications

References 26 publications

Verification as Learning Geometric Concepts

Verification as Learning Geometric Concepts

ResAna: a resource analysis toolset for (real‐time) JAVA

Neural State Classification for Hybrid Systems

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