scholarly journals Abstract Interpretation with Infinitesimals: Towards Scalability in Nonstandard Static Analysis

10.29007/rls3 ◽  
2018 ◽  
Author(s):  
Kengo Kido ◽  
Swarat Chaudhuri ◽  
Ichiro Hasuo
Keyword(s):  
Hybrid Systems ◽  
Static Analysis ◽  
Abstract Interpretation ◽  
Analysis Program ◽  
Deductive Verification ◽  
Prototype Implementation ◽  
Hybrid Dynamics ◽  
Verification Tools ◽  
Widening Operators ◽  
Theoretical Results

Towards the goal of correctness and reliability of hybrid systems, we continue our nonstandard static analysis program (with Suenaga and Sekine) where hybrid dynamics is turned into purely discrete one with explicit use of infinitesimals. While our previous results have focused on deductive verification by program logics, the current work aims at automation and enhanced scalability by extending abstract interpretation—a technique known for its ample scalability and widespread use in various verification tools—with infinitesimals. Our theoretical results include soundness and termination via uniform widening operators; and our prototype implementation successfully verifies some benchmark examples.

A Survey of Parametric Static Analysis

2021 ◽  
Vol 54 (7) ◽  
pp. 1-37
Author(s):  
Jihyeok Park ◽  
Hongki Lee ◽  
Sukyoung Ryu
Keyword(s):  
Recent Work ◽  
Static Analysis ◽  
Abstract Interpretation ◽  
Black Box ◽  
Parameter Selection ◽  
Survey Analysis ◽  
Future Directions ◽  
Analysis Techniques ◽  
Analysis Quality

Understanding program behaviors is important to verify program properties or to optimize programs. Static analysis is a widely used technique to approximate program behaviors via abstract interpretation. To evaluate the quality of static analysis, researchers have used three metrics: performance, precision, and soundness. The static analysis quality depends on the analysis techniques used, but the best combination of such techniques may be different for different programs. To find the best combination of analysis techniques for specific programs, recent work has proposed parametric static analysis . It considers static analysis as black-box parameterized by analysis parameters , which are techniques that may be configured without analysis details. We formally define the parametric static analysis, and we survey analysis parameters and their parameter selection in the literature. We also discuss open challenges and future directions of the parametric static analysis.

Verification of Non-Functional Requirements by Abstract Interpretation

2012 ◽  
pp. 22-35
Author(s):  
Agostino Cortesi ◽  
Francesco Logozzo
Keyword(s):  
Static Analysis ◽  
Abstract Interpretation ◽  
Software Requirements ◽  
Functional Requirements ◽  
Formal Approach ◽  
Space Efficiency ◽  
Source Program ◽  
Service Oriented ◽  
Abstract Domains ◽  
Functional Software

This chapter investigates a formal approach to the verification of non-functional software requirements that are crucial in Service-oriented Systems, like portability, time and space efficiency, and dependability/robustness. The key-idea is the notion of observable, i.e., an abstraction of the concrete semantics when focusing on a behavioral property of interest. By applying an abstract interpretation-based static analysis of the source program, and by a suitable choice of abstract domains, it is possible to design formal and effective tools for non-functional requirements validation.

scholarly journals Soundness, idempotence and commutativity of set-sharing

2002 ◽  
Vol 2 (2) ◽  
pp. 155-201 ◽  
Author(s):  
PATRICIA M. HILL ◽  
ROBERTO BAGNARA ◽  
ENEA ZAFFANELLA
Keyword(s):  
Logic Programming ◽  
Abstract Interpretation ◽  
Theoretical Study ◽  
Data Flow ◽  
Practical Work ◽  
Mathematical Framework ◽  
Generic Properties ◽  
Set Sharing ◽  
Theoretical Results

It is important that practical data-flow analyzers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined and sound with respect to the concrete semantics. In logic programming, the abstract domain Sharing is a standard choice for sharing analysis for both practical work and further theoretical study. In spite of this, we found that there were no satisfactory proofs for the key properties of commutativity and idempotence that are essential for Sharing to be well-defined and that published statements of the soundness of Sharing assume the occurs-check. This paper provides a generalization of the abstraction function for Sharing that can be applied to any language, with or without the occurs-check. Results for soundness, idempotence and commutativity for abstract unification using this abstraction function are proven.

scholarly journals Optimality in goal-dependent analysis of Sharing

2009 ◽  
Vol 9 (05) ◽  
pp. 617-689 ◽  
Author(s):  
GIANLUCA AMATO ◽  
FRANCESCA SCOZZARI
Keyword(s):  
Logic Programming ◽  
Static Analysis ◽  
Abstract Interpretation ◽  
Logic Programs ◽  
Semantic Operators

AbstractWe face the problems of correctness, optimality, and precision for the static analysis of logic programs, using the theory of abstract interpretation. We propose a framework with a denotational, goal-dependent semantics equipped with two unification operators for forward unification (calling a procedure) and backward unification (returning from a procedure). The latter is implemented through a matching operation. Our proposal clarifies and unifies many different frameworks and ideas on static analysis of logic programming in a single, formal setting. On the abstract side, we focus on the domainsharingby Jacobs and Langen (The Journal of Logic Programming, 1992, vol. 13, nos. 2–3, pp. 291–314) and provide the best correct approximation of all the primitive semantic operators, namely, projection, renaming, and forward and backward unifications. We show that the abstract unification operators are strictly more precise than those in the literature defined over the same abstract domain. In some cases, our operators are more precise than those developed for more complex domains involving linearity and freeness.

scholarly journals ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

10.29007/zkf6 ◽  
2020 ◽  
Author(s):  
Luca Geretti ◽  
Julien Alexandre Dit Sandretto ◽  
Matthias Althoff ◽  
Luis Benet ◽  
Alexandre Chapoutot ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Formal Verification ◽  
Hybrid Systems ◽  
Reachability Analysis ◽  
Current Status ◽  
Benchmark Problems ◽  
Hybrid Dynamics ◽  
Friendly Competition

We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. This year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. These tools are applied to solve reachability analysis problems on six benchmark problems, two of them featuring hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.

scholarly journals Static Analysis for ECMAScript String Manipulation Programs

2020 ◽  
Vol 10 (10) ◽  
pp. 3525 ◽  
Author(s):  
Vincenzo Arceri ◽  
Isabella Mastroeni ◽  
Sunyi Xu
Keyword(s):  
Static Analysis ◽  
Abstract Interpretation ◽  
Finite State Automata ◽  
Language Program ◽  
Object Property ◽  
Wide Range ◽  
Dynamic Languages ◽  
Finite State ◽  
Dynamic Language

In recent years, dynamic languages, such as JavaScript or Python, have been increasingly used in a wide range of fields and applications. Their tricky and misunderstood behaviors pose a great challenge for static analysis of these languages. A key aspect of any dynamic language program is the multiple usage of strings, since they can be implicitly converted to another type value, transformed by string-to-code primitives or used to access an object-property. Unfortunately, string analyses for dynamic languages still lack precision and do not take into account some important string features. In this scenario, more precise string analyses become a necessity. The goal of this paper is to place a first step for precisely handling dynamic language string features. In particular, we propose a new abstract domain approximating strings as finite state automata and an abstract interpretation-based static analysis for the most common string manipulating operations provided by the ECMAScript specification. The proposed analysis comes with a prototype static analyzer implementation for an imperative string manipulating language, allowing us to show and evaluate the improved precision of the proposed analysis.

scholarly journals Goblint: Thread-Modular Abstract Interpretation Using Side-Effecting Constraints

2021 ◽  
pp. 438-442
Author(s):  
Simmo Saan ◽  
Michael Schwarz ◽  
Kalmer Apinis ◽  
Julian Erhard ◽  
Helmut Seidl ◽  
...  
Keyword(s):  
Static Analysis ◽  
Abstract Interpretation ◽  
Analysis Framework ◽  
Data Race ◽  
C Programs ◽  
Global Invariants ◽  
Race Analysis

AbstractGoblintis a static analysis framework for C programs specializing in data race analysis. It relies on thread-modular abstract interpretation where thread interferences are accounted for by means of flow-insensitive global invariants.

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