Optimal Simulations Between Unary Automata
Carlo Mereghetti and Giovanni Pighizzini
Dipartimento di Scienze dell'Informazione
Università degli Studi di Milano
via Comelico 39 -- 20135 Milano, Italy
We consider the problem of computing the costs --- in terms of states ---
of optimal simulations between different kinds of
finite automata recognizing unary languages.
Our main result is a tight simulation of unary n-state two-way
nondeterministic automata by O(e^\sqrt(n \ln n))-state one-way
deterministic automata. In addition, we show that,
given a unary n-state two-way nondeterministic automaton, one can construct
an equivalent O(n^2)-state two-way nondeterministic automaton performing
both input head reversals and nondeterministic choices at the endmarkers only.
Further results on simulating unary alternating finite automata are pointed
Our results give answers to some questions left open in the literature.