Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce notions of simulation beten semiring-ighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo—hence soundness against language inclusion comes for free—but are concretely presented as matrices that are subject to linear inequality constraints. Pervasiveness of these formalisms allows us to exploit existing algorithms in: searching for a simulation, and hence verifying quantitative correctness that is formulated as language inclusion. Transformations of automata that aid search for simulations are introduced, too. This verification workflow is implemented for the plus-times and max-plus semirings. Furthermore, an extension to ighted  tree  automata is presented and implemented.
['Natsuki Urabe', 'Ichiro Hasuo']
I am writing a research paper on a idea Quantitative simulations by matrices
[{"from": "human", "value": "I am writing a research paper on a idea Quantitative simulations by matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce notions of simulation beten semiring-ighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo\u2014hence soundness against language inclusion comes for free\u2014but are concretely presented as matrices that are subject to linear inequality constraints. Pervasiveness of these formalisms allows us to exploit existing algorithms in: searching for a simulation, and hence verifying quantitative correctness that is formulated as language inclusion. Transformations of automata that aid search for simulations are introduced, too. This verification workflow is implemented for the plus-times and max-plus semirings. Furthermore, an extension to ighted  tree  automata is presented and implemented."}]