# Structural Refinement for the Modal nu-Calculus

@inproceedings{Fahrenberg2014StructuralRF, title={Structural Refinement for the Modal nu-Calculus}, author={Ulrich Fahrenberg and Axel Legay and Louis-Marie Traonouez}, booktitle={ICTAC}, year={2014} }

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent.

## 9 Citations

### 30 Years of Modal Transition Systems: Survey of Extensions and Analysis

- Computer ScienceModels, Algorithms, Logics and Tools
- 2017

The specification formalism of modal transition systems (MTS) is surveyed, various extensions of MTS, their relationships and modelling capabilities are discussed, and problems arising in verification and analysis of these systems are discussed.

### Behavioral Specification Theories: an Algebraic Taxonomy

- MathematicsISoLA
- 2020

This work starts by clarifying what precisely constitutes a behavioral specification theory and then introduces logical and structural operations and develops the resulting algebraic properties.

### ACTL for Modal Interface Automata

- Computer Science2016 16th International Conference on Application of Concurrency to System Design (ACSD)
- 2016

### Compositionality for quantitative specifications

- Computer ScienceFACS
- 2014

This work provides a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy based on disjunctive modal transition systems and shows how to compute the results of standard operations on the systems, including the quotient, which has not been previously considered for quantitative non-deterministic systems.

### A linear-time-branching-time spectrum for behavioral specification theories

- MathematicsJ. Log. Algebraic Methods Program.
- 2020

### A Linear-Time-Branching-Time Spectrum of Behavioral Specification Theories

- MathematicsSOFSEM
- 2017

It is shown that specification theories for preorders cannot exist and a general scheme is developed which allows us to define behavioral specification theories, based on disjunctive modal transition systems, for most equivalences in the linear-time–branching-time spectrum.

### Observational Refinement and Merge for Disjunctive MTSs

- Computer ScienceATVA
- 2016

Disjunctive MTS (DMTS) is an extension of MTS that has been getting attention in recent years, and a key concept for (D)MTS is refinement, supporting a development process where abstract specifications are gradually refined into more concrete ones.

### Petri net synthesis and modal specifications

- Computer Science
- 2018

It is shown that that the synthesis problem for mts and the ν-calculus is undecidable, but by restricting the Petri nets considered, the synthesis Problem becomes decidable even for the more expressive μ-Calculus.

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