Abstract
By modifying the acceptability conditions in finite automata, a new and equivalent variant the “structure automaton”is obtained. The collection SR(Σ) of sets of tapes on Σdefinable by deterministic structure automata forms, however, a proper subset of the collection of regular sets. The structure and closure properties of SR(Σ) are analyzed in detail, using a natural topology on Σ*, in which the closed sets are the reverse ultimately definite sets. A set of tapes V is in SR(2Σ) iff it is a finite union of regular “convex” sets. SR(Σ) is closed under Boolean operations, but not closed under product, star, or transpose operations. In fact, SR(Σ) is exactly the Boolean closure of the regular closed sets. The “signature” of a set is also defined and it is shown that a regular V is In SR(Σ) iff it has finite signature. Decision problems are also treated.
| Original language | English |
|---|---|
| Pages (from-to) | 1218-1227 |
| Number of pages | 10 |
| Journal | IEEE Transactions on Computers |
| Volume | C-23 |
| Issue number | 12 |
| DOIs | |
| State | Published - Dec 1974 |
| Externally published | Yes |
Keywords
- Closed regular sets
- convex languages
- definite and ultimately definite sets
- finite automata
- languages with finite signatures
- minimal regular sets
- open regular sets
- structure automata