Probabilistic semantics and program analysis

Authors:
Alessandra Di Pierro;Chris Hankin;Herbert Wiklicky
Affiliations:
University of Verona, Verona, Italy;Imperial College London, London, United Kingdom;Imperial College London, London, United Kingdom
Venue:
SFM'10 Proceedings of the Formal methods for quantitative aspects of programming languages, and 10th international conference on School on formal methods for the design of computer, communication and software systems
Year:
2010

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Abstract

The aims of these lecture notes are two-fold: (i) we investigate the relation between the operational semantics of probabilistic programming languages and Discrete Time Markov Chains (DTMCs), and (ii) we present a framework for probabilistic program analysis which is inspired by the classical Abstract Interpretation framework by Cousot & Cousot and which we introduced as Probabilistic Abstract Interpretation (PAI) in [1]. The link between programming languages and DTMCs is the construction of a so-called Linear Operator semantics (LOS) in a syntax-directed or compositional way. The main element in this construction is the use of tensor product to combine information about different aspects of a program. Although this inevitably results in a combinatorial explosion of the size of the semantics of program, the PAI approach allows us to keep some control and to obtain reasonably sized abstract models.