Towards a unified view of bisimulation: a comparative study

Roggenbach, Markus; Majster-Cederbaum, Mila

doi:10.1016/s0304-3975(99)00303-5

Cited by 30 publications

(22 citation statements)

References 28 publications

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“…They are employed today in a many areas of computer science, such as functional languages, object-oriented languages, types, data types, domains, databases, compiler optimizations, program analysis, verification tools, etc. For more information about bisimulations we refer to [1,26,53,62,95,100,101,120,126].…”

Section: Simulation and Bisimulationmentioning

confidence: 99%

Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey

Ignjatović

Ćirić

2012

Filomat

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Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneous weakly linear systems have been discussed in two recent papers. Here we give a brief overview of the main results from these two papers, as well as from a series of papers on applications of weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy automata, and in the social network analysis. Especially, we present algorithms for computing the greatest solutions to weakly linear systems.

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Section: Simulation and Bisimulationmentioning

confidence: 99%

Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey

Ignjatović

Ćirić

2012

Filomat

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“…Many algorithms have been proposed to compute the greatest bisimulation equivalence on a given labelled graph or a labelled transition system (cf. [43,[47][48][49]52,58,60]). The faster algorithms are based on the crucial equivalence between the greatest bisimulation equivalence and the relational coarsest partition problem ✩ Research supported by Ministry of Science and Technological Development, Republic of Serbia, Grant No.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy relation equations and reduction of fuzzy automata

Ćirić

Stamenković

Ignjatović

et al. 2010

Journal of Computer and System Sciences

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We show that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states. This system may consist of infinitely many equations, and finding its non-trivial solutions may be a very difficult task. For that reason we aim our attention to some instances of this system which consist of finitely many equations and are easier to solve. First, we study right invariant fuzzy equivalences, and their duals, the left invariant ones. We prove that each fuzzy automaton possesses the greatest right (resp. left) invariant fuzzy equivalence, which provides the best reduction by means of fuzzy equivalences of this type, and we give an effective procedure for computing this fuzzy equivalence, which works if the underlying structure of truth values is a locally finite residuated lattice. Moreover, we show that even better reductions can be achieved alternating reductions by means of right and left invariant fuzzy equivalences. We also study strongly right and left invariant fuzzy equivalences, which give worse reductions than right and left invariant ones, but whose computing is much easier. We give an effective procedure for computing the greatest strongly right (resp. left) invariant fuzzy equivalence, which is applicable to fuzzy automata over an arbitrary complete residuated lattice.

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“…If one chooses a map f which is the identity on inputs we recover the notion of bisimulation in [10]. Several other approaches to bisimulation are reported in the literature and we point the reader to the comparative study in [13] and the references therein. The notion of simulation allows to define several different types of abstraction since when f : M X − → M Y defines a simulation from Φ X to Φ Y , the map f B takes state trajectories of Φ X to state trajectories of Φ Y [15].…”

Section: Definition 3 (Simulations Of Abstract Control Systemsmentioning

confidence: 91%

Composing Abstractions of Hybrid Systems

Tabuada

Pappas

Lima

2002

Hybrid Systems: Computation and Control

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Abstract. The analysis and design of hybrid systems must exploit their hierarchical and compositional nature of in order to tackle complexity. In previous work, we presented a hierarchical abstraction framework for hybrid control systems based on the notions of simulation and bisimulation. In this paper, we build upon our previous work and investigate the compositionality of our abstraction framework. We present a composition operator that allows synchronization on inputs and states of hybrid systems. We then show that the composition operator is compatible with our abstraction framework in the sense that abstracting subsystems will the result in an abstraction of the overall system.

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Towards a unified view of bisimulation: a comparative study

Cited by 30 publications

References 28 publications

Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey

Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey

Fuzzy relation equations and reduction of fuzzy automata

Composing Abstractions of Hybrid Systems

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