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A Theory of Slicing for Imperative Probabilistic Programs

Authors:

Anindya BanerjeeAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 42, Issue 2

Article No.: 6, Pages 1 - 71

https://doi.org/10.1145/3372895

Published: 17 April 2020 Publication History

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Abstract

Dedicated to the memory of Sebastian Danicic.

We present a theory for slicing imperative probabilistic programs containing random assignments and “observe” statements for conditioning. We represent such programs as probabilistic control-flow graphs (pCFGs) whose nodes modify probability distributions. This allows direct adaptation of standard machinery such as data dependence, postdominators, relevant variables, and so on, to the probabilistic setting. We separate the specification of slicing from its implementation:

(1) first, we develop syntactic conditions that a slice must satisfy (they involve the existence of another disjoint slice such that the variables of the two slices are probabilistically independent of each other);

(2) next, we prove that any such slice is semantically correct;

(3) finally, we give an algorithm to compute the least slice.

To generate smaller slices, we may in addition take advantage of knowledge that certain loops will terminate (almost) always.

Our results carry over to the slicing of structured imperative probabilistic programs, as handled in recent work by Hur et al. For such a program, we can define its slice, which has the same “normalized” semantics as the original program; the proof of this property is based on a result proving the adequacy of the semantics of pCFGs w.r.t. the standard semantics of structured imperative probabilistic programs.

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Cited By

Amtoft TBanerjee A(2025)A Fixed Point Iteration Technique for Proving Correctness of Slicing for Probabilistic ProgramsLanguages, Compilers, Analysis - From Beautiful Theory to Useful Practice10.1007/978-3-032-08187-2_6(101-113)Online publication date: 25-Nov-2025
https://doi.org/10.1007/978-3-032-08187-2_6
Olmedo F(2025)Slicing of Probabilistic Programs: A Review of Existing ApproachesACM Computing Surveys10.1145/376458158:3(1-40)Online publication date: 28-Aug-2025
https://dl.acm.org/doi/10.1145/3764581
Tang CShuai HYang M(2025)Program Defect Detection Using Sensitive Slice Semantics with Control Flow Variable DependencyRecent Advances in Computer Science and Communications10.2174/012666255832126724072609322818:4Online publication date: Apr-2025
https://doi.org/10.2174/0126662558321267240726093228
Show More Cited By

Index Terms

A Theory of Slicing for Imperative Probabilistic Programs
1. Software and its engineering
  1. Software organization and properties
    1. Software functional properties
      1. Correctness
      2. Formal methods
        Automated static analysis
2. Theory of computation
  1. Models of computation
    1. Probabilistic computation
  2. Semantics and reasoning
    1. Program semantics

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