Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show how up-to techniques for (bi-)similarity can be used in the setting of ighted systems. The problems  consider are language equivalence, language inclusion and the threshold problem (also known as universality problem) for ighted automata. #R##N# build a bisimulation relation on the fly and work up-to congruence and up-to similarity. This requires to determine whether a pair of vectors (over a semiring) is in the congruence closure of a given relation of vectors. This problem is considered for rings and l-monoids, for the latter  provide a rewriting algorithm and show its confluence and termination. #R##N# then explain how to apply these up-to techniques to ighted automata and provide runtime results.
['Filippo Bonchi', 'Barbara König', 'Sebastian Küpper']
I am writing a research paper on a idea Up-To Techniques for Weighted Systems (Extended Version)
[{"from": "human", "value": "I am writing a research paper on a idea Up-To Techniques for Weighted Systems (Extended Version)"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show how up-to techniques for (bi-)similarity can be used in the setting of ighted systems. The problems  consider are language equivalence, language inclusion and the threshold problem (also known as universality problem) for ighted automata. #R##N# build a bisimulation relation on the fly and work up-to congruence and up-to similarity. This requires to determine whether a pair of vectors (over a semiring) is in the congruence closure of a given relation of vectors. This problem is considered for rings and l-monoids, for the latter  provide a rewriting algorithm and show its confluence and termination. #R##N# then explain how to apply these up-to techniques to ighted automata and provide runtime results."}]