Subset construction — where it appears
Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.
The exponential is in the expression
The subset construction on one family reaches two to the k plus one states, exactly and not approximately. A literal of the same length gives eleven. Both are regular expressions and the difference is that one of them asks the machine to remember something.
Where the table starts paying
Five thousand and sixty-five operations before the first character, then one per character. Against nothing before the first character and thirty-nine per character. They cross at two hundred and fifty-six characters, and that crossing is what an engine's compile decision actually is.
A cache below the reachable set
A lazy machine with a cache of two hundred and fifty-six states costs fifty-one operations a character and a plain non-deterministic simulation costs fifty-three. At five hundred and twelve it costs eleven. The line is flat across two orders of magnitude and then falls off a cliff.
Named alongside it
The objects these essays reach for when they reach for this one.
AutomatonDeterministic automatonCrossing pointLazy constructionNondeterministic automatonState explosionCacheLower boundRegular-expression