Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library

Bagnara, Roberto; Ricci, Elisa; Zaffanella, Enea; Hill, Patricia M.

doi:10.1007/3-540-45789-5_17

Cited by 91 publications

(91 citation statements)

References 19 publications

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“…In practice, we use PPL (the Parma Polyhedra Library [3]) to overapproximate the differential equations by rectangular inclusions. PPL is a C++ library to manipulate polyhedrons with large rational coefficients and exact arithmetic.…”

Section: Case Studymentioning

confidence: 99%

Automatic Rectangular Refinement of Affine Hybrid Systems

Doyen

Henzinger

Raskin

2005

Lecture Notes in Computer Science

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Abstract. We show how to automatically construct and refine rectangular abstractions of systems of linear differential equations. From a hybrid automaton whose dynamics are given by a system of linear differential equations, our method computes automatically a sequence of rectangular hybrid automata that are increasingly precise overapproximations of the original hybrid automaton. We prove an optimality criterion for successive refinements. We also show that this method can take into account a safety property to be verified, refining only relevant parts of the state space. The practicability of the method is illustrated on a benchmark case study.

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Section: Case Studymentioning

confidence: 99%

Automatic Rectangular Refinement of Affine Hybrid Systems

Doyen

Henzinger

Raskin

2005

Lecture Notes in Computer Science

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“…Since la−j −1 takes its maximal value when la is maximal and j is minimal, the expression la 0 −1 is an upper bound for la−j −1 . This can be done automatically using linear constraints tools [6]. Given a cost equation C(x)=exp+ k i=0 C(y i ), ϕ and an invariant C(x 0 );C(x), Ψ , the function below computes an upper bound for exp by maximizing its nat components.…”

Section: Upper Bounds On Cost Expressionsmentioning

confidence: 99%

“…A sufficient condition for a cost relation falling into the divide and conquer class is that each cost expression that is contributed by an equation is greater than or equal to the sum of the cost expressions contributed by the corresponding immediate recursive calls. This check is implemented in our prototype using [6]. Consider a CRS with the two equations C(n)=0, {n≤ 0} and C(n) = nat(n)+C(n 1 )+C(n 2 ), ϕ where ϕ={n>0, n 1 +n 2 +1≤n, n≥2 * n 1 , n ≥2 * n 2 , n 1 ≥0, n 2 ≥0}.…”

Section: Improving Accuracy In Divide and Conquer Programsmentioning

confidence: 99%

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Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis

et al.

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Abstract. The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, we first produce recurrence relations (RRs) which capture the cost of our program in terms of the size of its input data. Second, we convert such RRs into closed form (i.e., without recurrences). Whereas the first phase has received considerable attention, with a number of cost analyses available for a variety of programming languages, the second phase has received comparatively little attention. In this paper we first study the features of RRs generated by automatic cost analysis and discuss why existing computer algebra systems are not appropriate for automatically obtaining closed form solutions nor upper bounds of them. Then we present, to our knowledge, the first practical framework for the fully automatic generation of reasonably accurate upper bounds of RRs originating from cost analysis of a wide range of programs. It is based on the inference of ranking functions and loop invariants and on partial evaluation.

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“…To solve the linear constraint systems, we use the Parma Polyhedral Library (PPL) [1]. In general, solving a linear constraint system is exponential in the number of inequalities.…”

Section: Analyzing Effects Of Code Sequencesmentioning

confidence: 99%

Static Disassembly and Code Analysis

Vigna

Advances in Information Security

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Summary. The classification of an unknown binary program as malicious or benign requires two steps. In the first step, the stream of bytes that constitutes the program has to be transformed (or disassembled) into the corresponding sequence of machine instructions. In the second step, based on this machine code representation, static or dynamic code analysis techniques can be applied to determine the properties and function of the program.Both the disassembly and code analysis steps can be foiled by techniques that obfuscate the binary representation of a program. Thus, robust techniques are required that deliver reliable results under such adverse circumstances. In this chapter, we introduce a disassemble technique that can deal with obfuscated binaries. Also, we introduce a static code analysis approach that can identify high-level semantic properties of code that are difficult to conceal.

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Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library

Cited by 91 publications

References 19 publications

Automatic Rectangular Refinement of Affine Hybrid Systems

Automatic Rectangular Refinement of Affine Hybrid Systems

Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis

Static Disassembly and Code Analysis

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