Integrating Abstraction Techniques for Formal Verification of Analog Designs

Zaki, Mohamed H.; Denman, William; Tahar, Sofiène; Bois, Guy

doi:10.2514/1.44289

Cited by 5 publications

(5 citation statements)

References 34 publications

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“…The semi-algebraic abstraction [32] is a qualitative abstraction [34,37]. In this work, we propose a different algorithm to verify semi-algebraic abstractions that allows us to explore the abstract state-space symbolically, in contrast to the LazyReach algorithm [32].…”

Section: Related Workmentioning

confidence: 99%

Implicit Semi-Algebraic Abstraction for Polynomial Dynamical Systems

Mover

Cimatti

Griggio

et al. 2021

Computer Aided Verification

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Semi-algebraic abstraction is an approach to the safety verification problem for polynomial dynamical systems where the state space is partitioned according to the sign of a set of polynomials. Similarly to predicate abstraction for discrete systems, the number of abstract states is exponential in the number of polynomials. Hence, semi-algebraic abstraction is expensive to explicitly compute and then analyze (e.g., to prove a safety property or extract invariants).In this paper, we propose an implicit encoding of the semi-algebraic abstraction, which avoids the explicit enumeration of the abstract states: the safety verification problem for dynamical systems is reduced to a corresponding problem for infinite-state transition systems, allowing us to reuse existing model-checking tools based on Satisfiability Modulo Theory (SMT). The main challenge we solve is to express the semi-algebraic abstraction as a first-order logic formula that is linear in the number of predicates, instead of exponential, thus letting the model checker lazily explore the exponential number of abstract states with symbolic techniques. We implemented the approach and validated experimentally its potential to prove safety for polynomial dynamical systems.

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Section: Related Workmentioning

confidence: 99%

Implicit Semi-Algebraic Abstraction for Polynomial Dynamical Systems

Mover

Cimatti

Griggio

et al. 2021

Computer Aided Verification

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“…The benchmark suite consists of 141 continuous safety verification problems, with 90 earlier problems [78] and 51 new ones, all drawn from the literature [5,15,18,21,26,28,30,32,33,36,41,42,50,69,76,89,90,91]. Some of the problems are drawn from papers that present and discuss properties of a system of ODEs without explicitly providing initial and safe conditions; in such cases, we design our own initial and safe sets based on the provided discussion.…”

Section: Benchmark Suitementioning

confidence: 99%

“…Unlike first integrals, only p = 0 is guaranteed to be an invariant of the system. Darboux polynomials have been used for predicate abstraction of continuous systems by Zaki et al [91], who successfully applied them to verify electrical circuit designs. The problem of generating Darboux polynomials is generally far more difficult than that of generating polynomial first integrals (which represent the special case of Darboux polynomials where the cofactor α is 0 in the equation p = αp).…”

Section: Darboux Polynomialsmentioning

confidence: 99%

“…Tiwari further studied reachability of linear systems [81], using information from real eigenvectors and ideas from qualitative abstraction to generate invariants. Zaki et al [91] were the first to apply Darboux polynomials to verification of continuous systems using discrete abstraction. Numerous works employ barrier certificates for verification [15,37,61,77,89].…”

Section: Phmentioning

confidence: 99%

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Pegasus: A Framework for Sound Continuous Invariant Generation

Sogokon

Mitsch

Tan

et al. 2019

Lecture Notes in Computer Science

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Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without unrolling their loops forever, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to the automation of formal proofs of safety for hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.1 An etymological note on naming conventions. The KeY [3] prover provided the foundation for developing KeYmaera [58], an interactive theorem prover for hybrid systems. The name KeYmaera was a pun on the Chimera, a hybrid monster from Classical Greek mythology. The tactic language of the new (aXiomatic) KeYmaera X prover [24] is called Bellerophon [23], after the hero who defeats the Chimera in the myth. In keeping with an established tradition, the invariant generation framework is called Pegasus because the aid of this winged horse was crucial to the hero Bellerophon in his feat.

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“…Formal approaches like [11], [12], [13], [14], [15], [16] and semiformal approaches like [1], [2], [3], [17] are two main branches in the field. Mathematical origins of these approaches have Maler and Nickovic [18], [19] presented Signal Temporal Logic, STL, to monitor temporal properties of continuous signals by extending Metric Interval Time Logic, MITL [10].…”

Section: Related Workmentioning

confidence: 99%

Using haloes in mixed-signal assertion based verification

Ulus

Şen

2012

2012 IEEE International High Level Design Validation and Test Workshop (HLDVT)

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Abstract-We develop an assertion based verification solution for analog mixed-signal designs. We introduce the halo concept for analog signals to express them with their tolerance and variation values in assertions. The halo of a signal provides a relaxation over the signal and it defines an effective region for that signal which can be used in assertion based verification. Using haloes for analog signals allow us to define a new set of comparison relations between two analog signals including their equivalence. In our intended design flow, these new analog signal operators are placed into the Analog layer of mixed-signal assertion languages as an extension. We present experimental results on a programmable switch and a VCO.

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Integrating Abstraction Techniques for Formal Verification of Analog Designs

Cited by 5 publications

References 34 publications

Implicit Semi-Algebraic Abstraction for Polynomial Dynamical Systems

Implicit Semi-Algebraic Abstraction for Polynomial Dynamical Systems

Pegasus: A Framework for Sound Continuous Invariant Generation

Using haloes in mixed-signal assertion based verification

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