Completeness in abstract interpretation: A domain perspective

Giacobazzi, Roberto; Ranzato, Francesco

doi:10.1007/bfb0000474

Cited by 26 publications

(15 citation statements)

References 24 publications

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“…The fixpoint semantics of LO allows us to investigate in more depth the relationships between LO and DLP. For this purpose, we can employ the mathematical tools provided by abstract interpretation (Cousot & Cousot, 1977), and in particular the notion of completeness (Cousot & Cousot, 1977;Giacobazzi & Ranzato, 1997) that qualifies the precision of an abstraction. Informally, the comparison between LO and DLP fixpoint semantics is based on the abstraction that maps multisets into sets of atomic formulas (positive clauses).…”

Section: Dlp As Abstraction Of Lomentioning

confidence: 99%

“…This new representation enables the calculation of the abstract semantics in finite time, although it implies some loss of precision. We recall here some key concepts in abstract interpretation, which the reader can find in (Cousot & Cousot, 1977;Cousot & Cousot, 1979;Giacobazzi & Ranzato, 1997).…”

Section: Dlp As Abstraction Of Lomentioning

confidence: 99%

“…It can be proved that for a fixed concrete semantics, (full) completeness of an abstract interpretation only depends on the choice of the abstract domain. The problem of achieving a (fully) complete abstract interpretation starting from a correct one, by either refining or simplifying the abstract domain, is studied in (Giacobazzi & Ranzato, 1997). We conclude by observing that an equivalent presentation of abstract interpretation is based on closure operators (Cousot & Cousot, 1979), i.e.…”

Section: Dlp As Abstraction Of Lomentioning

confidence: 99%

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An effective fixpoint semantics for linear logic programs

Bozzano

Delzanno

Martelli

2001

Theory and Practice of Logic Programming

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In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977;Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

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Section: Dlp As Abstraction Of Lomentioning

confidence: 99%

Section: Dlp As Abstraction Of Lomentioning

confidence: 99%

Section: Dlp As Abstraction Of Lomentioning

confidence: 99%

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An effective fixpoint semantics for linear logic programs

Bozzano

Delzanno

Martelli

2001

Theory and Practice of Logic Programming

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“…The necessary and sufficient conditions embodied in minimisers appeasr to be closely related to the notion of completeness in abstract interpretation [13], where a minimiser m plays the role of a complete abstraction. It is to be noted that some work in the domain of quantitative information flow aiming at automated discovery of leaks also rely on analysis of equivalence classes [5,21].…”

Section: Related Workmentioning

confidence: 99%

Data Minimisation: A Language-Based Approach

Antignac

Sands

Schneider

2017

ICT Systems Security and Privacy Protection

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Data minimisation is a privacy-enhancing principle considered as one of the pillars of personal data regulations. This principle dictates that personal data collected should be no more than necessary for the specific purpose consented by the user. In this paper we study data minimisation from a programming language perspective. We assume that a given program embodies the purpose of data collection, and define a data minimiser as a pre-processor for the input which reduces the amount of information available to the program without compromising its functionality. In this context we study formal definitions of data minimisation, present different mechanisms and architectures to ensure data minimisation, and provide a procedure to synthesise a correct data minimiser for a given program.

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“…At the same time, Theorem 3.5 guarantees that our analysis is most precise for the code that LGen generates, meaning that each aligned memory access in the generated code is detected by our analysis and is handled by the appropriate aligned instruction. In other words, our analysis can be characterized as optimal or complete [18] with respect to the type of code that LGen generates.…”

Section: Alignment Detectionmentioning

confidence: 99%

A Basic Linear Algebra Compiler for Embedded Processors

Kyrtatas

Spampinato

Püschel

2015

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2015

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In many fields, such as signal processing, control, and graphics, there is a significant demand for efficient Dense Linear Algebra (DLA) code for embedded devices. At the same time, code generators have proved to be useful for generating fast DLA code for general-purpose computers. An example is LGen, a research compiler designed after Spiral for basic linear algebra computations of fixed size. In this thesis, we extend LGen towards four processors that are widely used in the embedded ecosystem: Intel Atom, ARM Cortex-A8, ARM Cortex-A9, and ARM1176. For this purpose, we introduce into the LGen methodology a set of optimizations that take into account the specific limitations and capabilities of these processors, aiming at generating highly optimized code for them. An extensive set of experiments run on our target platforms shows that the new version of LGen produces code that performs better than well-established, commercial and non-commercial libraries (Intel MKL and Intel IPP), software generators (Eigen and ATLAS), and compilers (icc, gcc, and clang).The large number of experiments that we conducted on the four investigated processors were executed using Mediator, a web-based middleware that was developed as part of this thesis. Mediator offers a RESTful interface that makes possible the simultaneous execution of experiments on multiple SSH-accessible devices by multiple users. More specifically, it guarantees mutual exclusion of the experiments running on a specific core, while at the same time applies load balancing over the cores of a device. On top of that, it also provides an easy-to-use mechanism for retrieving performance metrics on a variety of architectures with minimal user involvement.

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Completeness in abstract interpretation: A domain perspective

Cited by 26 publications

References 24 publications

An effective fixpoint semantics for linear logic programs

An effective fixpoint semantics for linear logic programs

Data Minimisation: A Language-Based Approach

A Basic Linear Algebra Compiler for Embedded Processors

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