Understanding Probabilistic Programs

We present two views of probabilistic programs and their relationship. An operational interpretation as well as a weakest pre-condition semantics are provided for an elementary probabilistic guarded command language. Our study treats important features such as sampling, conditioning, loop divergence, and non-determinism.

[1]  A. Pfeffer,et al.  Figaro : An Object-Oriented Probabilistic Programming Language , 2009 .

[2]  Dan Grossman,et al.  Expressing and verifying probabilistic assertions , 2014, PLDI.

[3]  Chung-Kil Hur,et al.  Slicing probabilistic programs , 2014, PLDI.

[4]  Gilles Barthe,et al.  Probabilistic Relational Reasoning for Differential Privacy , 2012, TOPL.

[5]  Frank D. Wood,et al.  A Compilation Target for Probabilistic Programming Languages , 2014, ICML.

[6]  Annabelle McIver,et al.  Linear-Invariant Generation for Probabilistic Programs: - Automated Support for Proof-Based Methods , 2010, SAS.

[7]  Micha Sharir,et al.  Verification of Probabilistic Programs , 1984, SIAM J. Comput..

[8]  Annabelle McIver,et al.  Probabilistic Guarded Commands Mechanized in HOL , 2005, Electron. Notes Theor. Comput. Sci..

[9]  Sriram Sankaranarayanan,et al.  Expectation Invariants for Probabilistic Program Loops as Fixed Points , 2014, SAS.

[10]  Joost-Pieter Katoen,et al.  On the Hardness of Almost-Sure Termination , 2015, MFCS.

[11]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[12]  Annabelle McIver,et al.  Conditioning in Probabilistic Programming , 2015, MFPS.

[13]  Thomas A. Henzinger,et al.  Probabilistic programming , 2014, FOSE.

[14]  Yishai A. Feldman,et al.  A probabilistic dynamic logic , 1982, STOC '82.

[15]  K RajamaniSriram,et al.  Slicing probabilistic programs , 2014 .

[16]  Dexter Kozen,et al.  Semantics of probabilistic programs , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[17]  Claudio V. Russo,et al.  Tabular: a schema-driven probabilistic programming language , 2014, POPL.

[18]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[19]  Holger Hermanns,et al.  Probabilistic Termination , 2015, POPL.

[20]  Edsger W. Dijkstra,et al.  A Discipline of Programming , 1976 .

[21]  Annabelle McIver,et al.  Abstraction, Refinement and Proof for Probabilistic Systems , 2004, Monographs in Computer Science.

[22]  Chung-Kil Hur,et al.  R2: An Efficient MCMC Sampler for Probabilistic Programs , 2014, AAAI.

[23]  Annabelle McIver,et al.  Operational versus weakest pre-expectation semantics for the probabilistic guarded command language , 2014, Perform. Evaluation.

[24]  David Cock,et al.  Verifying Probabilistic Correctness in Isabelle with pGCL , 2012, SSV.

[25]  Victor Shoup,et al.  A computational introduction to number theory and algebra , 2005 .

[26]  Ernst-Rüdiger Olderog,et al.  Nets, Terms and Formulas: Three Views of Concurrent Processes and their Relationship , 2005 .