Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
10.1007/978-3-031-77019-7_1guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
Article

Probabilistic Datatypes

Published: 25 November 2024 Publication History

Abstract

An encapsulated datatype collects related data together with the operations used to access them. Datatype refinement then provides a clear separation between the expectations of programs that call the operations (i.e. from outside the encapsulation) and the implementation of the operations themselves (inside the encapsulation), and it enforces consistency between the two.
In this paper we consider encapsulated probabilistic datatypes, i.e. those whose operations can “flip coins”; and we find as a result that the interface between calling programs’ expectations and their encapsulated probabilistic implementations must now provide consistency not only for functional properties but also for properties related to information flow.
In this paper we use a quantitative information-flow model for programs to give a sound basis for refinement of probabilistic datatypes.

References

[1]
Abrial, J.-R., Börger, E., Langmaak, H.: Formal Methods for Industrial Applications: Specifying and Programming the Steam Boiler Control, LNCS, vol. 1165. Springer (1996)
[2]
Alvim, M., Chatzikokolakis, K., McIver, A.K., Morgan, C.C., Smith, G.S., Palamidessi, C.: The science of quantitative information flow. In: Information Security and Cryptography. Springer (2020)
[3]
Alvim, M.S., Chatzikokolakis, K., Palamidessi, C., Smith, G.S.: Measuring information leakage using generalized gain functions. In: Proceedings of 25th IEEE Computer Security Foundations Symposium (CSF 2012), pp. 265–279 (2012)
[4]
Apt KR and Olderog E-R Fifty years of Hoare’s logic Formal Aspects Comput. 2019 31 751-807
[5]
Köpf, B.B., Basin, D.: An information-theoretic model for adaptive side-channel attacks. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, CCS ’07, pp. 286–296, New York, NY, USA. ACM (2007)
[6]
Back R-JR and von Wright J Refinement Calculus: a Systematic Introduction 1998 Springer
[7]
Backus JW et al. Report on the algorithmic language ALGOL 60 Commun. ACM 1960 3 5 299-311
[8]
Chatterjee K and Chmelík M POMDPs under probabilistic semantics Artif. Intell. 2015 221 46-72
[9]
Clark D, Hunt S, and Malacaria P Quantitative information flow, relations and polymorphic types J. Log. Comput. 2005 15 2 181-199
[10]
Dijkstra EW A Discipline of Programming 1976 Prentice-Hall
[11]
Gardiner PHB and Morgan CC Data refinement of predicate transformers Theor. Comput. Sci. 1991 87 143-62
[12]
Gardiner PHB and Morgan CC A single complete rule for data refinement Formal Aspects Comput. 1993 5 4 367-82
[13]
Gibbons J, McIver AK, Morgan CC, and Schrijvers T Barthe ASG and Katoen J-P Quantitative information flow with monads in Haskell Foundations of Probabilistic Programming 2019 CUP
[14]
Giry, M.: A categorical approach to probability theory. In: Categorical Aspects of Topology and Analysis, Lecture Notes in Mathematics, vol. 915, pp. 68–85. Springer (1981)
[15]
Gretz F, Katoen J-P, and McIver AK Operational versus weakest pre-expectation semantics for the probabilistic guarded command language Perform. Eval. 2014 73 110-132
[16]
Hoare CAR An axiomatic basis for computer programming Commun. ACM 1969 12 10 576-583
[17]
Jurado, M., Palamidessi, C., Smith, G.S.: A formal information-theoretic leakage analysis of order-revealing encryption. In: 34th IEEE Computer Security Foundations Symposium, CSF 2021, Dubrovnik, Croatia, June 21–25, 2021, pp. 1–16. IEEE (2021)
[18]
Kaminski, B.L.: Advanced Weakest Precondition Calculi for Probabilistic Programs. PhD thesis, RWTH Aachen University, Germany (2019)
[19]
Köpf, B., Smith, G.S: Vulnerability bounds and leakage resilience of blinded cryptography under timing attacks. In: Proceedings of the 23rd IEEE Computer Security Foundations Symposium, CSF 2010, Edinburgh, United Kingdom, July 17–19, 2010, pp. 44–56 (2010)
[20]
Kwiatkowska M, Norman G, and Parker D Probabilistic symbolic model checking with PRISM: a hybrid approach Int. J. Softw. Tools Technol. Transf. (STTT) 2004 6 2 128-42
[21]
Larsen KG and Skou A Bisimulation through probabilistic testing Inf. Comput. 1991 94 1 1-28
[22]
Malacaria P Risk assessment of security threats for looping constructs J. Comput. Secur. 2010 18 2 191-228
[23]
McIver, A.K.,Meinicke, L.A., Morgan, C.C.: Compositional Closure for Bayes Risk in Probabilistic Noninterference. Draft full version of [24] with appendices (2010). arXiv:1007.1054v1
[24]
McIver A, Meinicke L, and Morgan C Abramsky S, Gavoille C, Kirchner C, Meyer auf der Heide F, and Spirakis PG Compositional closure for Bayes Risk in probabilistic noninterference Automata, Languages and Programming 2010 Heidelberg Springer 223-235
[25]
McIver, A.K., Meinicke, L.A., Morgan, C.C.: A Kantorovich-monadic powerdomain for information hiding, with probability and nondeterminism. In: Processdings of LICS 2012 (2012)
[26]
McIver AK and Morgan CC Abstraction, Refinement and Proof for Probabilistic Systems 2005 New York Springer
[27]
McIver AK, Morgan CC, and Troubitsyna E Grundy J, Schwenke M, and Vickers T The probabilistic steam boiler: a case study in probabilistic data refinement Proceedings International Refinement Workshop, ANU, Canberra 1998 Springer 250-65
[28]
McIver, A., Morgan, C., Rabehaja, T.: Abstract hidden Markov models: a monadic account of quantitative information flow. In: Proceedings of LICS 2015 (2015)
[29]
Morgan CC Programming from Specifications 1994 2 Prentice Hall
[30]
Morgan CC, McIver AK, and Seidel K Probabilistic predicate transformers ACM Trans. Prog. Lang. Sys. 1996 18 3 325-53
[31]
Morgan CC and Vickers TN On the Refinement Calculus 1994 Berlin Springer
[32]
Morris JM A theoretical basis for stepwise refinement and the programming calculus Sci. Comput. Program. 1987 9 3 287-306
[33]
Nipkow T Non-deterministic data types: models and implementations Acta Informatica 1986 22 6 629-661
[34]
Smith G de Alfaro L On the foundations of quantitative information flow Foundations of Software Science and Computational Structures 2009 Heidelberg Springer 288-302

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings
Theoretical Aspects of Computing – ICTAC 2024: 21st International Colloquium, Bangkok, Thailand, November 25–29, 2024, Proceedings
Nov 2024
416 pages
ISBN:978-3-031-77018-0
DOI:10.1007/978-3-031-77019-7

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 25 November 2024

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 0
    Total Downloads
  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 13 Jan 2025

Other Metrics

Citations

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media