Reachability analysis using multiway decision graphs in the HOL theorem prover

2008 ◽  
Author(s):  
Sa'ed Abed ◽  
Otmane Ait Mohamed ◽  
Ghiath Al Sammane
Keyword(s):  
Reachability Analysis ◽  
Theorem Prover ◽  
Multiway Decision Graphs ◽  
Hol Theorem Prover

CSim 2

2021 ◽  
Vol 43 (1) ◽  
pp. 1-46
Author(s):  
David Sanan ◽  
Yongwang Zhao ◽  
Shang-Wei Lin ◽  
Liu Yang
Keyword(s):  
Programming Languages ◽  
Concurrent Systems ◽  
Theorem Prover ◽  
Compositional Techniques ◽  
Machine Code ◽  
Top Down ◽  
Hol Theorem Prover ◽  
High Level ◽  
High Degree

To make feasible and scalable the verification of large and complex concurrent systems, it is necessary the use of compositional techniques even at the highest abstraction layers. When focusing on the lowest software abstraction layers, such as the implementation or the machine code, the high level of detail of those layers makes the direct verification of properties very difficult and expensive. It is therefore essential to use techniques allowing to simplify the verification on these layers. One technique to tackle this challenge is top-down verification where by means of simulation properties verified on top layers (representing abstract specifications of a system) are propagated down to the lowest layers (that are an implementation of the top layers). There is no need to say that simulation of concurrent systems implies a greater level of complexity, and having compositional techniques to check simulation between layers is also desirable when seeking for both feasibility and scalability of the refinement verification. In this article, we present CSim 2 a (compositional) rely-guarantee-based framework for the top-down verification of complex concurrent systems in the Isabelle/HOL theorem prover. CSim 2 uses CSimpl, a language with a high degree of expressiveness designed for the specification of concurrent programs. Thanks to its expressibility, CSimpl is able to model many of the features found in real world programming languages like exceptions, assertions, and procedures. CSim 2 provides a framework for the verification of rely-guarantee properties to compositionally reason on CSimpl specifications. Focusing on top-down verification, CSim 2 provides a simulation-based framework for the preservation of CSimpl rely-guarantee properties from specifications to implementations. By using the simulation framework, properties proven on the top layers (abstract specifications) are compositionally propagated down to the lowest layers (source or machine code) in each concurrent component of the system. Finally, we show the usability of CSim 2 by running a case study over two CSimpl specifications of an Arinc-653 communication service. In this case study, we prove a complex property on a specification, and we use CSim 2 to preserve the property on lower abstraction layers.

scholarly journals Tool Presentation: Isabelle/HOL for Reachability Analysis of Continuous Systems

10.29007/b3wr ◽  
2018 ◽  
Author(s):  
Fabian Immler
Keyword(s):  
Distinctive Feature ◽  
Reachability Analysis ◽  
Theorem Prover ◽  
Continuous Systems ◽  
Affine Arithmetic ◽  
Discretization Errors ◽  
Runge Kutta

We present a tool for reachability analysis of continuous systems based onaffine arithmetic and Runge-Kutta methods. The distinctive feature of our toolis its verification in the interactive theorem prover Isabelle/HOL: thealgorithm is guaranteed to compute safe overapproximations, taking into accountall round-off and discretization errors.

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