The entropy of finite-state \(\omega\)-languages. (English) Zbl 0582.94012

Staiger, L.

Probl. Control Inf. Theory 14, 383-392 (1985).

In the present paper we prove that the entropy (or channel capacity) is countably ”additive” in the case of finite-state \(\omega\)-languages. From this result we further obtain a topological characterization of finite- state \(\omega\)-languages belonging to certain entropy levels.

MSC:

94A17	Measures of information, entropy
68Q45	Formal languages and automata

Keywords:

finite-state languages; omega languages; channel capacity; topological characterization