Dynamic cut-off algorithm for parameterised refinement checking

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


Research units

  • University of Oulu
  • University of Helsinki


The verification of contemporary software systems is challenging, because they are heavily parameterised containing components, the number and connections of which cannot be a priori fixed. We consider the multi-parameterised verification of safety properties by refinement checking in the context of labelled transition systems (LTSs). The LTSs are parameterised by using first-order constructs, sorts, variables, and predicates, while preserving compositionality. This allows us to parameterise not only the number of replicated components but also the system topology, the connections between the components. We aim to solve a verification task in the parameterised LTS formalism by determining cut-offs for the parameters. As the main contribution, we convert this problem into the unsatisfiability of a first-order formula and provide a SAT modulo theories (SMT)-based semi-algorithm for dynamically, i.e., iteratively, computing the cut-offs. The algorithm will always terminate for topologies expressible in the ∃ * ∀ * fragment of first-order logic. It also enables us to consider systems with topologies beyond this fragment, but for these systems, the algorithm is not guaranteed to terminate. We have implemented the approach on top of the Z3 SMT solver and successfully applied it to several system models. As a running example, we consider the leader election phase of the Raft consensus algorithm and prove a cut-off of three servers which we conjecture to be the optimal one.


Original languageEnglish
Title of host publicationFormal Aspects of Component Software - 15th International Conference, FACS 2018, Proceedings
Publication statusPublished - 1 Jan 2018
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Formal Aspects of Component Software - Pohang, Korea, Republic of
Duration: 10 Oct 201812 Oct 2018
Conference number: 15

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11222 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Conference on Formal Aspects of Component Software
Abbreviated titleFACS
CountryKorea, Republic of

    Research areas

  • Compositional verification, Cut-off, First-order logic, Labelled transition systems, Parameterized systems, Refinement checking, Safety properties, Satisfiability modulo theories

ID: 29118431