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Ignacio Fábregas

Publications and source records attributed to Ignacio Fábregas.

14 recordsLinked to original sources
arXiv2024

Logical characterisations, rule formats and compositionality for input-output conformance simulation

Input-output conformance simulation (iocos) has been proposed by Gregorio-Rodríguez, Llana and Martínez-Torres as a simulation-based behavioural preorder underlying model-based testing. This relation is inspired by Tretmans' classic ioco relation, but has better worst-case complexity than ioco and supports stepwise refinement. The goal of this paper is to develop the theory of iocos by studying logical characterisations of this relation, rule formats for it and its compositionality. More specifically, this article presents characterisations of iocos in terms of modal logics and compares them with an existing logical characterisation for ioco proposed by Beohar and Mousavi. It also offers a characteristic-formula construction for iocos over finite processes in an extension of the proposed modal logics with greatest fixed points. A precongruence rule format for iocos and a rule format ensuring that operations take quiescence properly into account are also given. Both rule formats are based on the GSOS format by Bloom, Istrail and Meyer. The general modal decomposition methodology of Fokkink and van Glabbeek is used to show how to check the satisfaction of properties expressed in the logic for iocos in a compositional way for operations specified by rules in the precongruence rule format for iocos .

cs.LO↗
arXiv2024

On the specification of modal systems: A comparison of three frameworks

This paper studies the relationships between three notions of behavioural preorder that have been proposed in the literature: refinement over modal transition systems, and the covariant-contravariant simulation and the partial bisimulation preorders over labelled transition systems. It is shown that there are mutual translations between modal transition systems and labelled transition systems that preserve, and reflect, refinement and the covariant-contravariant simulation preorder. The translations are also shown to preserve the modal properties that can be expressed in the logics that characterize those preorders. A translation from labelled transition systems modulo the partial bisimulation preorder into the same model modulo the covariant-contravariant simulation preorder is also offered, together with some evidence that the former model is less expressive than the latter. In order to gain more insight into the relationships between modal transition systems modulo refinement and labelled transition systems modulo the covariant-contravariant simulation preorder, their connections are also phrased and studied in the context of institutions.

cs.LO↗
arXiv2024

When Are Prime Formulae Characteristic?

In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic formulae, are exactly the consistent and prime ones. This paper presents general, sufficient conditions guaranteeing that characteristic formulae are exactly the consistent and prime ones. It is shown that the given conditions apply to various behavioural relations in the literature. In particular, characteristic formulae are exactly the prime and consistent ones for all the semantics in van Glabbeek's linear time-branching time spectrum.

cs.LO↗
arXiv2024

Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations

Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the paper: a natural transformation from a functor F to another G transforms F-bisimulations into G-bisimulations but, in general, it is not possible to express G-bisimulations in terms of F-bisimulations. However, they can be characterized by considering Hughes and Jacobs' notion of simulation, taking as the order on the functor F the equivalence induced by the epi-mono decomposition of the natural transformation relating F and G. We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial way, and extend all these results to categorical simulations.

cs.LO↗
arXiv2024

Reflection and Preservation of Properties in Coalgebraic (bi)Simulations

Our objective is to extend the standard results of preservation and reflection of properties by bisimulations to the coalgebraic setting, as well as to study under what conditions these results hold for simulations. The notion of bisimulation is the classical one, while for simulations we use that proposed by Hughes and Jacobs. As for properties, we start by using a generalization of linear temporal logic to arbitrary coalgebras suggested by Jacobs, and then an extension by Kurtz which includes atomic propositions too.

cs.LO↗
arXiv2024

Non-strongly Stable Orders Also Define Interesting Simulation Relations

We present a study of the notion of coalgebraic simulation introduced by Hughes and Jacobs. Although in their original paper they allow any functorial order in their definition of coalgebraic simulation, for the simulation relations to have good properties they focus their attention on functors with orders which are strongly stable. This guarantees a so-called "composition-preserving" property from which all the desired good properties follow. We have noticed that the notion of strong stability not only ensures such good properties but also "distinguishes the direction" of the simulation. For example, the classic notion of simulation for labeled transition systems, the relation "p is simulated by q", can be defined as a coalgebraic simulation relation by means of a strongly stable order, whereas the opposite relation, "p simulates q", cannot. Our study was motivated by some interesting classes of simulations that illustrate the application of these results: covariant-contravariant simulations and conformance simulations.

cs.LO↗
arXiv2024

Logics for Contravariant Simulations

Covariant-contravariant simulation and conformance simulation are two generalizations of the simple notion of simulation which aim at capturing the fact that it is not always the case that "the larger the number of behaviors, the better". Therefore, they can be considered to be more adequate to express the fact that a system is a correct implementation of some specification. We have previously shown that these two more elaborated notions fit well within the categorical framework developed to study the notion of simulation in a generic way. Now we show that their behaviors have also simple and natural logical characterizations, though more elaborated than those for the plain simulation semantics.

cs.LO↗
arXiv2024

Rule Formats for Nominal Process Calculi

The nominal transition systems (NTSs) of Parrow et al. describe the operational semantics of nominal process calculi. We study NTSs in terms of the nominal residual transition systems (NRTSs) that we introduce. We provide rule formats for the specifications of NRTSs that ensure that the associated NRTS is an NTS and apply them to the operational specification of the early pi-calculus. Our study stems from the recent Nominal SOS of Cimini et al. and from earlier works in nominal sets and nominal logic by Gabbay, Pitts and their collaborators.

cs.LO↗
arXiv2021

On Algebraic Abstractions for Concurrent Separation Logics

Concurrent separation logic is distinguished by transfer of state ownership upon parallel composition and framing. The algebraic structure that underpins ownership transfer is that of partial commutative monoids (PCMs). Extant research considers ownership transfer primarily from the logical perspective while comparatively less attention is drawn to the algebraic considerations. This paper provides an algebraic formalization of ownership transfer in concurrent separation logic by means of structure-preserving partial functions (i.e., morphisms) between PCMs, and an associated notion of separating relations. Morphisms of structures are a standard concept in algebra and category theory, but haven't seen ubiquitous use in separation logic before. Separating relations are binary relations that generalize disjointness and characterize the inputs on which morphisms preserve structure. The two abstractions facilitate verification by enabling concise ways of writing specs, by providing abstract views of threads' states that are preserved under ownership transfer, and by enabling user-level construction of new PCMs out of existing ones.

cs.PL↗
arXiv2019

Specifying Concurrent Programs in Separation Logic: Morphisms and Simulations

In addition to pre- and postconditions, program specifications in recent separation logics for concurrency have employed an algebraic structure of resources---a form of state transition system---to describe the state-based program invariants that must be preserved, and to record the permissible atomic changes to program state. In this paper we introduce a novel notion of resource morphism, i.e. structure-preserving function on resources, and show how to effectively integrate it into separation logic, using an associated notion of morphism-specific simulation. We apply morphisms and simulations to programs verified under one resource, to compositionally adapt them to operate under another resource, thus facilitating proof reuse.

cs.PL↗
arXiv2019

Rule Formats for Nominal Process Calculi

The nominal transition systems (NTSs) of Parrow et al. describe the operational semantics of nominal process calculi. We study NTSs in terms of the nominal residual transition systems (NRTSs) that we introduce. We provide rule formats for the specifications of NRTSs that ensure that the associated NRTS is an NTS and apply them to the operational specifications of the early and late pi-calculus. We also explore alternative specifications of the NTSs in which we allow residuals of abstraction sort, and introduce translations between the systems with and without residuals of abstraction sort. Our study stems from the Nominal SOS of Cimini et al. and from earlier works in nominal sets and nominal logic by Gabbay, Pitts and their collaborators.

cs.LO↗
arXiv2011

Graphical representation of covariant-contravariant modal formulae

Covariant-contravariant simulation is a combination of standard (covariant) simulation, its contravariant counterpart and bisimulation. We have previously studied its logical characterization by means of the covariant-contravariant modal logic. Moreover, we have investigated the relationships between this model and that of modal transition systems, where two kinds of transitions (the so-called may and must transitions) were combined in order to obtain a simple framework to express a notion of refinement over state-transition models. In a classic paper, Boudol and Larsen established a precise connection between the graphical approach, by means of modal transition systems, and the logical approach, based on Hennessy-Milner logic without negation, to system specification. They obtained a (graphical) representation theorem proving that a formula can be represented by a term if, and only if, it is consistent and prime. We show in this paper that the formulae from the covariant-contravariant modal logic that admit a "graphical" representation by means of processes, modulo the covariant-contravariant simulation preorder, are also the consistent and prime ones. In order to obtain the desired graphical representation result, we first restrict ourselves to the case of covariant-contravariant systems without bivariant actions. Bivariant actions can be incorporated later by means of an encoding that splits each bivariant action into its covariant and its contravariant parts.

cs.LO↗
arXiv2010

Equational Characterization of Covariant-Contravariant Simulation and Conformance Simulation Semantics

Covariant-contravariant simulation and conformance simulation generalize plain simulation and try to capture the fact that it is not always the case that "the larger the number of behaviors, the better". We have previously studied their logical characterizations and in this paper we present the axiomatizations of the preorders defined by the new simulation relations and their induced equivalences. The interest of our results lies in the fact that the axiomatizations help us to know the new simulations better, understanding in particular the role of the contravariant characteristics and their interplay with the covariant ones; moreover, the axiomatizations provide us with a powerful tool to (algebraically) prove results of the corresponding semantics. But we also consider our results interesting from a metatheoretical point of view: the fact that the covariant-contravariant simulation equivalence is indeed ground axiomatizable when there is no action that exhibits both a covariant and a contravariant behaviour, but becomes non-axiomatizable whenever we have together actions of that kind and either covariant or contravariant actions, offers us a new subtle example of the narrow border separating axiomatizable and non-axiomatizable semantics. We expect that by studying these examples we will be able to develop a general theory separating axiomatizable and non-axiomatizable semantics.

cs.LO↗