Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Quantitative aspects of systems like consumption of resources, output of goods, or reliability can be modeled by ighted automata. Recently, objectives like the average cost or the longtime peak por consumption of a system have been modeled by ighted automata which are not semiring ighted anymore. Instead, operations like limit superior, limit average, or discounting are used to determine the behavior of these automata. Here,  introduce a new class of ight structures subsuming a range of these models as ll as semirings. Our main result shows that such ighted automata and Kleene-type regular expressions are expressively equivalent both for finite and infinite words.
['Manfred Droste', 'Ingmar Meinecke']
I am writing a research paper on a idea WEIGHTED AUTOMATA AND REGULAR EXPRESSIONS OVER VALUATION MONOIDS
[{"from": "human", "value": "I am writing a research paper on a idea WEIGHTED AUTOMATA AND REGULAR EXPRESSIONS OVER VALUATION MONOIDS"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Quantitative aspects of systems like consumption of resources, output of goods, or reliability can be modeled by ighted automata. Recently, objectives like the average cost or the longtime peak por consumption of a system have been modeled by ighted automata which are not semiring ighted anymore. Instead, operations like limit superior, limit average, or discounting are used to determine the behavior of these automata. Here,  introduce a new class of ight structures subsuming a range of these models as ll as semirings. Our main result shows that such ighted automata and Kleene-type regular expressions are expressively equivalent both for finite and infinite words."}]