## A.: Coalgebraic Logic and Synthesis of Mealy Machines

Citations: | 10 - 7 self |

### BibTeX

@TECHREPORT{Bonsangue_a.:coalgebraic,

author = {M. M. Bonsangue and Jan Rutten and Ra Silva},

title = {A.: Coalgebraic Logic and Synthesis of Mealy Machines},

institution = {},

year = {}

}

### OpenURL

### Abstract

Abstract. We present a novel coalgebraic logic for deterministic Mealy machines that is sound, complete and expressive w.r.t. bisimulation. Every finite Mealy machine corresponds to a finite formula in the language. For the converse, we give a compositional synthesis algorithm which transforms every formula into a finite Mealy machine whose behaviour is exactly the set of causal functions satisfying the formula. 1

### Citations

343 |
R.: On the synthesis of a reactive module
- Pnueli, Rosner
- 1989
(Show Context)
Citation Context ...tion, for every formula in the logic, of a finite Mealy Machine whose behaviour is exactly characterised by the formula. 1.1 Related Work Automata synthesis is a popular and very active research area =-=[13,8,4,15,5]-=-. Most of the work done on synthesis has as main goal to find a proper and sufficiently expressive type of automata to encode a specific type of logic (such as LTL [15] or μ-calculus [8]). Technically... |

305 | An Automata-Theoretic Approach to Branching-Time Model Checking - Kupferman, Vardi, et al. - 2000 |

302 | Results on the Propositional µ-Calculus - Kozen - 1983 |

31 |
Duality for logics of transition systems
- Bonsangue, Kurz
- 2005
(Show Context)
Citation Context ...a consequence of [9, Theorem 2.1]. The modal fragment of our logic (i.e, the set of closed formulae without the ν operator) is a special case of the coalgebraic logic obtained by a Stone-type duality =-=[1,2]-=-. In what follows, we shall concentrate on the set Lc g of formulae that are both guarded and closed, that is, without free occurrences of fixed point variables x . We turn the set Lc g into a Mealy m... |

26 |
Presenting functors by operations and equations
- Bonsangue, Kurz
- 2006
(Show Context)
Citation Context ...tion of a final Mealy machine, in [14], as the set of all causal stream functions from A ω to B ω . Following coalgebraic methodology, we apply general insights from coalgebraic modal logic (see e.g. =-=[12,2]-=-) and define a logic whose basic operations derive directly from the functor M . The equivalence induced by the logic coincides with that induced by the functor M . Further, the logic comes equipped w... |

24 |
Coalgebraic logic, Annals of Pure and Applied Logic 96
- Moss
- 1999
(Show Context)
Citation Context ...tion of a final Mealy machine, in [14], as the set of all causal stream functions from A ω to B ω . Following coalgebraic methodology, we apply general insights from coalgebraic modal logic (see e.g. =-=[12,2]-=-) and define a logic whose basic operations derive directly from the functor M . The equivalence induced by the logic coincides with that induced by the functor M . Further, the logic comes equipped w... |

20 | µ-calculus synthesis
- Kupferman, Vardi
- 2000
(Show Context)
Citation Context ...tion, for every formula in the logic, of a finite Mealy Machine whose behaviour is exactly characterised by the formula. 1.1 Related Work Automata synthesis is a popular and very active research area =-=[13,8,4,15,5]-=-. Most of the work done on synthesis has as main goal to find a proper and sufficiently expressive type of automata to encode a specific type of logic (such as LTL [15] or μ-calculus [8]). Technically... |

19 | Algebraic specification and coalgebraic synthesis of mealy automata, in: L.B. Zhiming Liu (Ed
- Rutten
(Show Context)
Citation Context ...ht is that the properties of Mealy machines (coalgebras) are fully dictated by (the shape of) their defining functor M . This has led, for instance, to the identification of a final Mealy machine, in =-=[14]-=-, as the set of all causal stream functions from A ω to B ω . Following coalgebraic methodology, we apply general insights from coalgebraic modal logic (see e.g. [12,2]) and define a logic whose basic... |

13 | Y.: Coalgebraic automata theory: Basic results
- Kupke, Venema
- 2008
(Show Context)
Citation Context ...ting ϕ into an alternating automaton Aϕ, reducing Aϕ into a non-deterministic automaton which is then checked for non-emptiness [8]. The same process has been recently generalized to F -coalgebras in =-=[10]-=-. In this paper, we use a different approach. We construct a deterministic Mealy machine for a formula directly, by considering the formula as a state of the automaton containing enough information ab... |

9 | Synthesis of Mealy machines using derivatives
- Hansen, Costa, et al.
- 2006
(Show Context)
Citation Context ...tion, for every formula in the logic, of a finite Mealy Machine whose behaviour is exactly characterised by the formula. 1.1 Related Work Automata synthesis is a popular and very active research area =-=[13,8,4,15,5]-=-. Most of the work done on synthesis has as main goal to find a proper and sufficiently expressive type of automata to encode a specific type of logic (such as LTL [15] or μ-calculus [8]). Technically... |

8 | D.Wang. Executable Protocol Specification in ESL
- Clarke, German, et al.
- 2000
(Show Context)
Citation Context ...ich can be instantiated to Mealy machines. However, Mealy machines are typically “defined” in a natural language such as English. This obviously leads to ambiguities, inconsistencies and plain errors =-=[4]-=-. In this paper, we propose a simple but adequate and expressive logical language for the specification of Mealy machines. Here adequate means that the logical equivalence corresponds to a natural beh... |

5 |
Introduction to Logic Design
- Marcovitz
- 2005
(Show Context)
Citation Context ...tween such binary Mealy machines, on the one hand, and sequential digital circuits built out of logical gates and some kind of memory elements, on the other. In present day text books on logic design =-=[11]-=- — on the construction of sequential digital circuits — Mealy machines are still the most important mathematically exact means for the specification of the intended behaviour of circuits. There does n... |

3 |
A.: Compositional synthesis of generalized mealy machines
- Tini, Maggiolo-Schettini
- 2004
(Show Context)
Citation Context |

2 |
R.F.C.: Feedback, trace and fixed-point semantics
- Katis, Sabadini, et al.
- 2002
(Show Context)
Citation Context ...es not seem to exist, however, a generally accepted way of formally specifying Mealy machines themselves. The only formal approach we are aware of is the general model for categories with feedback in =-=[6]-=-, which can be instantiated to Mealy machines. However, Mealy machines are typically “defined” in a natural language such as English. This obviously leads to ambiguities, inconsistencies and plain err... |