Semantics, Logics, and Calculi pp 111-139

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9560) | Cite as

Probabilistic Abstract Interpretation: From Trace Semantics to DTMC’s and Linear Regression

Chapter

Abstract

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di VeronaVeronaItaly
  2. 2.Department of ComputingImperial College LondonLondonUK

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