Relating Modal Refinements, Covariant-Contravariant Simulations and Partial Bisimulations

Aceto, Luca; Fábregas, Ignacio; Frutos-Escrig, David de; Ingólfsdóttir, Anna; Palomino, Miguel

doi:10.1007/978-3-642-29320-7_18

Cited by 7 publications

(14 citation statements)

References 10 publications

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“…Then we observe that bivariant actions can be seen as the combination of a covariant and a contravariant action. In fact, this also corresponds with the idea used in [1] when relating MTSs and cc-systems. Indeed, the constraint imposed on must transitions in MTSs, where they should always be accompanied by their may counterparts, tells us somehow that they have a "nearly" bivariant behaviour.…”

Section: Introductionmentioning

confidence: 53%

“…Proof. We proved in [1] the corresponding result for T 0 and the transformation T 0 which is defined on logic formulae exactly as T , but renaming again each a ∈ A r into a r . From the definitions of T and T 0 we immediately conclude that a l -transitions with a ∈ A r do not play any role in the satisfaction of any formula T (ϕ), and then the result follows from that proved in [1].…”

Section: Proposition 2 T Preserves and Reflects The Cc-logic That Ismentioning

confidence: 92%

“…where all φ i j and ψ i k are also in normal form. In particular, ⊥ is obtained when I = / 0 and ⊤ when I = {1} and J 1…”

Section: Lemmamentioning

confidence: 99%

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Graphical representation of covariant-contravariant modal formulae

Aceto¹,

Fábregas²,

Frutos-Escrig³

et al. 2011

Electron. Proc. Theor. Comput. Sci.

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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 covariantcontravariant 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 covariantcontravariant 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.

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Section: Introductionmentioning

confidence: 53%

Section: Proposition 2 T Preserves and Reflects The Cc-logic That Ismentioning

confidence: 92%

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Graphical representation of covariant-contravariant modal formulae

Aceto¹,

Fábregas²,

Frutos-Escrig³

et al. 2011

Electron. Proc. Theor. Comput. Sci.

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“…We will employ this minimization to reduce the size of the uncontrolled system in a supervisory control framework that automatically synthesizes control software [14]. Furthermore, the algorithm can also serve as basis for computing minimization with respect to so-called covariant-contravariant simulations, which have recently been shown related to the notion of modal transition systems [18].…”

Section: Concluding Remarks and Discussionmentioning

confidence: 99%

Saving Time in a Space-Efficient Simulation Algorithm

Markovski

2011

2011 11th International Conference on Quality Software

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We present an efficient algorithm for computing the simulation preorder and equivalence for labeled transition systems. The algorithm improves an existing space-efficient algorithm and improves its time complexity by employing a variant of the stability condition and exploiting properties of the underlying relations and partitions. It has comparable space and time complexity with the most efficient counterpart algorithms for Kripke structures.

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“…It is worth noting that in [2], XY -simulation relations are called covariantcontravariant simulation relations.…”

Section: Definition 1 (Labeled Transition Systems)mentioning

confidence: 99%

A Pre-congruence Format for XY-simulation

Beohar

Mousavi

2015

Fundamentals of Software Engineering

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Abstract. XY -simulation is a generalization of bisimulation that is parameterized with two subsets of actions. XY -simulation is known in the literature under different names such as modal refinement, partial bisimulation, and alternating simulation. In this paper, we propose a precongruence rule format for XY -simulation. The format allows for checking compositionality of XY -simulation for an arbitrary language with structural operational semantics, by performing very simple checks on the syntactic shape of the rules. We apply our format to derive concrete compositionality results for different notions of behavioral pre-order with respect to different process calculi in the literature.

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Relating Modal Refinements, Covariant-Contravariant Simulations and Partial Bisimulations

Cited by 7 publications

References 10 publications

Graphical representation of covariant-contravariant modal formulae

Graphical representation of covariant-contravariant modal formulae

Saving Time in a Space-Efficient Simulation Algorithm

A Pre-congruence Format for XY-simulation

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