Details

Autor(en) / Beteiligte

• Lavado, Giovanna J.
• Pighizzini, Giovanni
• Seki, Shinnosuke

Titel

Converting nondeterministic automata and context-free grammars into Parikh equivalent one-way and two-way deterministic automata

Ist Teil von

• Information and computation, 2013-07, Vol.228-229, p.1-15

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2013

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with eO(n⋅lnn) and p(n) states, respectively, where p(n) is a polynomial. Furthermore, these costs are tight. In contrast, if all the words accepted by the given automaton contain at least two different letters, then a Parikh equivalent one-way deterministic automaton with a polynomial number of states can be found. Concerning context-free grammars, we prove that for each grammar in Chomsky normal form with h variables there exist Parikh equivalent one-way and two-way deterministic automata with 2O(h2) and 2O(h) states, respectively. Even these bounds are tight.