Simulations between cellular automata on Cayley graphs
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
On the capability of finite automata in 2 and 3 dimensional space
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Automata on a 2-dimensional tape
FOCS '67 Proceedings of the 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)
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In this paper, we consider the pebble automata introduced by Blum and Hewitt, but now moving through the unbounded plane Z^2. We are interested in their ability to recognize families of dotted figures. Contrary to the bounded case studied by Blum and Hewitt, the hierarchy collapses: there are families recognized with 0, 1, 2 and 3 pebbles, but each family recognized with more than three pebbles is recognized with exactly 3 ones. This result is connected to the existence of an intrinsically universal} 3-pebble-automaton. We formally define the underlying universality notion, and prove that there exists some 3-pebble automaton intrinsically universal, but no such automaton with only 2 pebbles.