In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems – yet it has remained severely limited in its applicability to more complex systems. We address the main problems of HyTech with PHAVer, a new tool for the exact verification of safety properties of hybrid systems with piecewise constant bounds on the derivatives. Affine dynamics are handled by on-the-fly overapproximation and by partitioning the state space based on user-definable constraints and the dynamics of the system. PHAVer's exact arithmetic is robust due to the use of the Parma Polyhedra Library, which supports arbitrarily large numbers. To manage the complexity of the polyhedral computations, we propose methods to conservatively limit the number of bits and constraints of polyhedra. Experimental results for a navigation benchmark and a tunnel diode circuit show the effectiveness of the approach.

/pdf/phaver-algorithmic-verification-of-hybrid-systems-past-54obela629.pdf

PHAVer: algorithmic verification of hybrid systems past hytech

https://www.cs.unipr.it/~bagnara/Papers/PDF/SCP08.pdf

The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems

This paper concerns static-analysis algorithms for analyzing x86 executables. The aim of the work is to recover intermediate representations that are similar to those that can be created for a program written in a high-level language. Our goal is to perform this task for programs such as plugins, mobile code, worms, and virus-infected code. For such programs, symbol-table and debugging information is either entirely absent, or cannot be relied upon if present; hence, the technique described in the paper makes no use of symbol-table/debugging information. Instead, an analysis is carried out to recover information about the contents of memory locations and how they are manipulated by the executable.

/pdf/analyzing-memory-accesses-in-x86-executables-b8k82wwqbl.pdf

Analyzing Memory Accesses in x86 Executables

In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems. But due to practical and systematic limitations it is only applicable to relatively simple systems. We address the main problems of HyTech with PHAVer, a new tool for the exact verification of safety properties of hybrid systems with piecewise constant bounds on the derivatives, so-called linear hybrid automata. Affine dynamics are handled by on-the-fly overapproximation and partitioning of the state space based on user-provided constraints and the dynamics of the system. PHAVer features exact arithmetic in a robust implementation that, based on the Parma Polyhedra Library, supports arbitrarily large numbers. To force termination and manage the complexity of the polyhedral computations, we propose methods to conservatively limit the number of bits and constraints of polyhedra. Experimental results for a navigation benchmark and a tunnel diode circuit demonstrate the effectiveness of the approach.

/pdf/phaver-algorithmic-verification-of-hybrid-systems-past-18kwxqqh0j.pdf

PHAVer: algorithmic verification of hybrid systems past HyTech

/pdf/abstract-interpretation-6cck59a5hy.pdf

Abstract interpretation

Linear Relation Analysis [11] is an abstract interpretation devoted to the automatic discovery of invariant linear inequalities among numerical variables of a program. In this paper, we apply such an analysis to the verification of quantitative time properties of two kinds of systems: synchronous programs and linear hybrid systems.

Verification of Real-Time Systems using Linear Relation Analysis

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Verification of Real-Time Systems using Linear Relation Analysis