2012/12/06 by Lavado, Giovanna J., Pighizzini, Giovanni, Seki, Shinnosuke
#F.1.1 #F.4.2 #F.4.3 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.1212.1346
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 ln n)) 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.