Converting Finite Width AFAs to Nondeterministic and Universal Finite Automata

The maximal existential (respectively, universal) width of an alternating finite automaton (AFA) on a string w is the maximal number of existential choices encountered in one branch (respectively, the maximal number of universal parallel branches) of a computation of A on w. We give upper bounds for the size of a nondeterministic finite automaton simulating an AFA of finite maximal universal width and for the size of a universal finite automaton simulating an AFA of finite maximal existential width. We give lower bounds for the transformations that are tight within a multiplicative factor that depends only on the universal (respectively, existential) width of the AFA.