TY - JOUR
T1 - Finite automata, definable sets, and regular expressions over ωn-tapes
AU - Choueka, Yaacov
PY - 1978/8
Y1 - 1978/8
N2 - The theory of finite automata and regular expressions over a finite alphabet Σ is here generalized to infinite tapes X = X1 ... Xk, where Xi, are themselves tapes of length ωn, for some n ≥ 0. Closure under the usual set-theoretical operations is established, and the equivalence of deterministic and nondeterministic automata is proved. A Kleene-type characterization of the definable sets is given and finite-length generalized regular expressions are developed for finitely denoting these sets. Decision problems are treated; a characterization Of regular tapes by multiperiodic sets is specified. Characterization by equivalence relations is discussed while stressing dissimilarities with the finite case.
AB - The theory of finite automata and regular expressions over a finite alphabet Σ is here generalized to infinite tapes X = X1 ... Xk, where Xi, are themselves tapes of length ωn, for some n ≥ 0. Closure under the usual set-theoretical operations is established, and the equivalence of deterministic and nondeterministic automata is proved. A Kleene-type characterization of the definable sets is given and finite-length generalized regular expressions are developed for finitely denoting these sets. Decision problems are treated; a characterization Of regular tapes by multiperiodic sets is specified. Characterization by equivalence relations is discussed while stressing dissimilarities with the finite case.
UR - http://www.scopus.com/inward/record.url?scp=0002698996&partnerID=8YFLogxK
U2 - 10.1016/0022-0000(78)90036-3
DO - 10.1016/0022-0000(78)90036-3
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AN - SCOPUS:0002698996
SN - 0022-0000
VL - 17
SP - 81
EP - 97
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
IS - 1
ER -