# On possibilities of one-way synchronized and alternating automata

## Abstract

Synchronized alternating machines generalize alternating ones, similarly alternating machines generalize nondeterministic ones. We are interested in the following questions: 1) what is the simplest kind of device working over the single-letter alphabet for which synchronized alternation is more powerful than alternation, and 2) what are minimal conditions on automata making the emptiness problem unsolvable?

We prove that even in the case of 1-way finite automata with one head, synchronized alternating automata accept nonregular (nonsemilinear) languages over the single-letter alphabet. The main result of this paper is that the emptiness problem for languages accepted by arbitrary 1-way synchronized alternating automata with only one head is unsolvable — even over the single letter alphabet.

The emptiness problem for languages over the single-letter alphabet accepted by arbitrary 1-way finite alternating k-head automata is unsolvable for k>2.

There are many measures of complexity that can be reduced to one with arbitrarily small multiplicative constant. For the leafsize of accepting trees of 1-way finite alternating multitape automata this is not true.

## Keywords

Internal State Finite Automaton Universal State Input Word Input Alphabet## Preview

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