Tradeoffs Between Reliability and Conciseness of Deterministic Finite Automata

In this paper, we propose a model for measuring the reliability of the description of a language by a deterministic finite automaton . Intuitively, the reliability exhibits when used for is high if the “difference” between and the language accepted by is small. Using this model, we prove that the savings in the number of states between a fully reliable and a less reliable representation cannot be bounded by any function, even if the unreliable descriptions are required to exceed any given fixed level of reliability. Furthermore, we show that, for a single regular language, there is a level of reliability such that any description exceeding this level is at least as big as the smallest DFA for the language.