Parameter Synthesis Algorithms for Parametric Interval Markov Chains

Laure Petrucci, Jaco van de Pol

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

45 Downloads (Pure)

Abstract

This paper considers the consistency problem for Parametric Interval Markov Chains. In particular, we introduce a co-inductive definition of consistency, which improves and simplifies previous inductive definitions considerably. The equivalence of the inductive and co-inductive definitions has been formally proved in the interactive theorem prover PVS. These definitions lead to forward and backward algorithms, respectively, for synthesizing an expression for all parameters for which a given PIMC is consistent. We give new complexity results when tackling the consistency problem for IMCs (i.e. without parameters). We provide a sharper upper bound, based on the longest simple path in the IMC. The algorithms are also optimized, using different techniques (dynamic programming cache, polyhedra representation, etc.). They are evaluated on a prototype implementation. For parameter synthesis, we use Constraint Logic Programming and the PARMA library for convex polyhedra.
Original languageEnglish
Title of host publicationFormal Techniques for Distributed Objects, Components, and Systems
Subtitle of host publication38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings
EditorsChristel Baier, Luis Caires
Place of PublicationCham
PublisherSpringer
Pages121-140
Number of pages20
ISBN (Electronic)978-3-319-92612-4
ISBN (Print)978-3-319-92611-7
DOIs
Publication statusPublished - Jun 2018
Event38th IFIP WG 6.1 International Conference, FORTE 2018 - University Complutense of Madrid, Madrid, Spain
Duration: 18 Jun 201821 Jun 2018
Conference number: 38
http://2018.discotec.org/index.html

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume10854

Conference

Conference38th IFIP WG 6.1 International Conference, FORTE 2018
Abbreviated titleFORTE 2018
CountrySpain
CityMadrid
Period18/06/1821/06/18
OtherHeld as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018
Internet address

Fingerprint

Inductive Definitions
Markov processes
Markov chain
Synthesis
Interval
Logic programming
Dynamic programming
Constraint Logic Programming
Convex polyhedron
Polyhedron
Cache
Dynamic Programming
Simplify
Equivalence
Prototype
Upper bound
Path
Theorem

Keywords

  • Parametric Interval Markov Chains
  • consistency checking
  • parameter synthesis
  • parma polyhedra library
  • constraint solving

Cite this

Petrucci, L., & van de Pol, J. (2018). Parameter Synthesis Algorithms for Parametric Interval Markov Chains. In C. Baier, & L. Caires (Eds.), Formal Techniques for Distributed Objects, Components, and Systems: 38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings (pp. 121-140). (Lecture Notes in Computer Science; Vol. 10854). Cham: Springer. https://doi.org/10.1007/978-3-319-92612-4_7
Petrucci, Laure ; van de Pol, Jaco. / Parameter Synthesis Algorithms for Parametric Interval Markov Chains. Formal Techniques for Distributed Objects, Components, and Systems: 38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings. editor / Christel Baier ; Luis Caires. Cham : Springer, 2018. pp. 121-140 (Lecture Notes in Computer Science).
@inproceedings{786bd7f632a047beb6b4432bf69b5ed9,
title = "Parameter Synthesis Algorithms for Parametric Interval Markov Chains",
abstract = "This paper considers the consistency problem for Parametric Interval Markov Chains. In particular, we introduce a co-inductive definition of consistency, which improves and simplifies previous inductive definitions considerably. The equivalence of the inductive and co-inductive definitions has been formally proved in the interactive theorem prover PVS. These definitions lead to forward and backward algorithms, respectively, for synthesizing an expression for all parameters for which a given PIMC is consistent. We give new complexity results when tackling the consistency problem for IMCs (i.e. without parameters). We provide a sharper upper bound, based on the longest simple path in the IMC. The algorithms are also optimized, using different techniques (dynamic programming cache, polyhedra representation, etc.). They are evaluated on a prototype implementation. For parameter synthesis, we use Constraint Logic Programming and the PARMA library for convex polyhedra.",
keywords = "Parametric Interval Markov Chains, consistency checking, parameter synthesis, parma polyhedra library, constraint solving",
author = "Laure Petrucci and {van de Pol}, Jaco",
year = "2018",
month = "6",
doi = "10.1007/978-3-319-92612-4_7",
language = "English",
isbn = "978-3-319-92611-7",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "121--140",
editor = "Christel Baier and Luis Caires",
booktitle = "Formal Techniques for Distributed Objects, Components, and Systems",

}

Petrucci, L & van de Pol, J 2018, Parameter Synthesis Algorithms for Parametric Interval Markov Chains. in C Baier & L Caires (eds), Formal Techniques for Distributed Objects, Components, and Systems: 38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings. Lecture Notes in Computer Science, vol. 10854, Springer, Cham, pp. 121-140, 38th IFIP WG 6.1 International Conference, FORTE 2018, Madrid, Spain, 18/06/18. https://doi.org/10.1007/978-3-319-92612-4_7

Parameter Synthesis Algorithms for Parametric Interval Markov Chains. / Petrucci, Laure; van de Pol, Jaco.

Formal Techniques for Distributed Objects, Components, and Systems: 38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings. ed. / Christel Baier; Luis Caires. Cham : Springer, 2018. p. 121-140 (Lecture Notes in Computer Science; Vol. 10854).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Parameter Synthesis Algorithms for Parametric Interval Markov Chains

AU - Petrucci, Laure

AU - van de Pol, Jaco

PY - 2018/6

Y1 - 2018/6

N2 - This paper considers the consistency problem for Parametric Interval Markov Chains. In particular, we introduce a co-inductive definition of consistency, which improves and simplifies previous inductive definitions considerably. The equivalence of the inductive and co-inductive definitions has been formally proved in the interactive theorem prover PVS. These definitions lead to forward and backward algorithms, respectively, for synthesizing an expression for all parameters for which a given PIMC is consistent. We give new complexity results when tackling the consistency problem for IMCs (i.e. without parameters). We provide a sharper upper bound, based on the longest simple path in the IMC. The algorithms are also optimized, using different techniques (dynamic programming cache, polyhedra representation, etc.). They are evaluated on a prototype implementation. For parameter synthesis, we use Constraint Logic Programming and the PARMA library for convex polyhedra.

AB - This paper considers the consistency problem for Parametric Interval Markov Chains. In particular, we introduce a co-inductive definition of consistency, which improves and simplifies previous inductive definitions considerably. The equivalence of the inductive and co-inductive definitions has been formally proved in the interactive theorem prover PVS. These definitions lead to forward and backward algorithms, respectively, for synthesizing an expression for all parameters for which a given PIMC is consistent. We give new complexity results when tackling the consistency problem for IMCs (i.e. without parameters). We provide a sharper upper bound, based on the longest simple path in the IMC. The algorithms are also optimized, using different techniques (dynamic programming cache, polyhedra representation, etc.). They are evaluated on a prototype implementation. For parameter synthesis, we use Constraint Logic Programming and the PARMA library for convex polyhedra.

KW - Parametric Interval Markov Chains

KW - consistency checking

KW - parameter synthesis

KW - parma polyhedra library

KW - constraint solving

U2 - 10.1007/978-3-319-92612-4_7

DO - 10.1007/978-3-319-92612-4_7

M3 - Conference contribution

SN - 978-3-319-92611-7

T3 - Lecture Notes in Computer Science

SP - 121

EP - 140

BT - Formal Techniques for Distributed Objects, Components, and Systems

A2 - Baier, Christel

A2 - Caires, Luis

PB - Springer

CY - Cham

ER -

Petrucci L, van de Pol J. Parameter Synthesis Algorithms for Parametric Interval Markov Chains. In Baier C, Caires L, editors, Formal Techniques for Distributed Objects, Components, and Systems: 38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings. Cham: Springer. 2018. p. 121-140. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-92612-4_7