Skip to main content
Kent Academic Repository

Deciding equivalence-based properties using constraint solving

Cheval, Vincent, Cortier, Véronique, Delaune, Stéphanie (2013) Deciding equivalence-based properties using constraint solving. Theoretical Computer Science, 492 . pp. 1-39. ISSN 0304-3975. (doi:10.1016/j.tcs.2013.04.016) (KAR id:46725)


Formal methods have proved their usefulness for analyzing the security of protocols. Most existing results focus on trace properties like secrecy or authentication. There are however several security properties, which cannot be defined (or cannot be naturally defined) as trace properties and require a notion of behavioural equivalence. Typical examples are anonymity, privacy related properties or statements closer to security properties used in cryptography.

In this paper, we consider three notions of equivalence defined in the applied pi calculus: observational equivalence, may-testing equivalence, and trace equivalence. First, we study the relationship between these three notions. We show that for determinate processes, observational equivalence actually coincides with trace equivalence, a notion simpler to reason with. We exhibit a large class of determinate processes, called simple processes, that capture most existing protocols and cryptographic primitives. While trace equivalence and may-testing equivalence seem very similar, we show that may-testing equivalence is actually strictly stronger than trace equivalence. We prove that the two notions coincide for image-finite processes, such as processes without replication.

Second, we reduce the decidability of trace equivalence (for finite processes) to deciding symbolic equivalence between sets of constraint systems. For simple processes without replication and with trivial else branches, it turns out that it is actually sufficient to decide symbolic equivalence between pairs of positive constraint systems. Thanks to this reduction and relying on a result first proved by M. Baudet, this yields the first decidability result of observational equivalence for a general class of equational theories (for processes without else branch nor replication). Moreover, based on another decidability result for deciding equivalence between sets of constraint systems, we get decidability of trace equivalence for processes with else branch for standard primitives.

Item Type: Article
DOI/Identification number: 10.1016/j.tcs.2013.04.016
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Q Science > QA Mathematics (inc Computing science) > QA 9 Formal systems, logics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Vincent Cheval
Date Deposited: 23 Jan 2015 11:29 UTC
Last Modified: 16 Nov 2021 10:18 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Cheval, Vincent.

Creator's ORCID:
CReDIT Contributor Roles:
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.