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Structure Automata
December 1974 (vol. 23 no. 12)
pp. 1218-1227
Y.A. Choueka, Department of Mathematics, University of Illinois
By modifying the acceptability conditions in finite automata, a new and equivalent variant?the "structure automaton"? is obtained. The collection SR(S) of sets of tapes on S definable by deterministic structure-automata forms, however, a proper subset of the collection of regular sets. The structure and closure properties of SR(S) are analyzed in detail, using a natural topology on S*, in which the closed sets are the reverse ultimately definite sets. A set of tapes V is in SR(S) iff it is a finite union of regular "convex" sets. SR(S) is closed under Boolean operations, but not-closed under product, star, or transpose operations. In fact, SR(S) is exactly the Boolean closure of the regular closed sets. The "sigture" of a set is also defined and it is shown that a regular V is in SR(S) iff it has finite signature. Decision problems are also treated.
Index Terms:
Closed regular sets, convex languages, definite and ultimately definite sets, finite automata, languages with finite signatures, minimal regular sets, open regular sets, structure automata.
Citation:
Y.A. Choueka, "Structure Automata," IEEE Transactions on Computers, vol. 23, no. 12, pp. 1218-1227, Dec. 1974, doi:10.1109/T-C.1974.223840
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