you mention motivations in comments but in this question you seem to be asking about how to determine worst case bounds on a/ the "compression ratio" of an unminimized DFA versus a minimized one. this is indeed studied systematically/ scientifically but note that an unminimized DFA can have unbounded redundant states so this question must be formalized more carefully/ cleverly to come up with some kind of metric.

here are two example papers in the area that study it empirically. the first is in the context of router systems that use DFA rules for examining packets. the 2^nd uses randomly generated DFAs somewhat analogous to Erdos-Renyi graphs and examines efficiency of different algorithms.

• Compressing Regular Expressions’ DFA Table by Matrix Decomposition / Liu, Liu, Tan

• On the performance of automata minimization algorithms / Almeida, Moreira, Reis

You mention motivations in comments, but in this question you seem to be asking about how to determine worst case bounds on a/the "compression ratio" of an unminimized DFA versus a minimized one. This is indeed studied systematically/scientifically but note that an unminimized DFA can have unbounded redundant states so this question must be formalized more carefully/cleverly to come up with some kind of metric.

Here are two example papers in the area that study it empirically. The first is in the context of router systems that use DFA rules for examining packets. The 2^nd uses randomly generated DFAs somewhat analogous to Erdos-Renyi graphs and examines efficiency of different algorithms.

• Compressing Regular Expressions’ DFA Table by Matrix Decomposition / Liu, Liu, Tan

• On the performance of automata minimization algorithms / Almeida, Moreira, Reis

you mention motivations in comments but in this question you seem to be asking about how to determine worst case bounds on a/ the "compression ratio" of an unminimized DFA versus a minimized one. this is indeed studied systematically/ scientifically but note that an unminimized DFA can have unbounded redundant states so this question must be formalized more carefully/ cleverly to come up with some kind of metric.

here are two example papers in the area that study it empirically. the first is in the context of router systems that use DFA rules for examining packets. the 2^nd uses randomly generated DFAs somewhat analogous to Erdos-Renyi graphs and examines efficiency of different algorithms.

• Compressing Regular Expressions’ DFA Table by Matrix Decomposition / Liu, Liu, Tan

• On the performance of automata minimization algorithms / Almeida, Moreira, Reis

you mention motivations in comments but in this question you seem to be asking about how to determine worst case bounds on a/ the "compression ratio" of an unminimized DFA versus a minimized one. this is indeed studied systematically/ scientifically but note that an unminimized DFA can have unbounded redundant states so this question must be formalized more carefully/ cleverly to come up with some kind of metric.

here are two example papers in the area that study it empirically. the first is in the context of router systems that use DFA rules for examining packets. the 2^nd uses randomly generated DFAs somewhat analogous to Erdos-Renyi graphs and examines efficiency of different algorithms.

• Compressing Regular Expressions’ DFA Table by Matrix Decomposition / Liu, Liu, Tan

• On the performance of automata minimization algorithms / Almeida, Moreira, Reis