One Pebble Does Not Suffice to Search Plane Labyrinths

In 1975 L. Budach proved in a groundbreaking paper ([7]) that there is no finite automaton which is able to search (to master) all finite (cofinite) plane labyrinths. On the other side we have a result of M. Blum, D. Kozen (1978, [4]) saying that the search can be implemented with just two pebbles. The aim of our paper is to show that one pebble does not suffice, answering a question of Blum,Kozen. Furthermore we present a new construction for universal traps (see H.Antelmann, L.Budach, H.-A.Rollik 1979, [2]).

[1]  Horst Müller.  Automata Catching Labyrinths with at most Three Components , 1979, J. Inf. Process. Cybern..

[2]  L. Budach.  Automata and Labyrinths , 1978 .

[3]  Lothar Budach,et al.  Environments, Labyrinths and Automata , 1977, FCT.

[4]  Günter Asser.  Bemerkungen zum Labyrinth-Problem , 1977, J. Inf. Process. Cybern..

[5]  Lothar Budach,et al.  On Universal Traps , 1979, J. Inf. Process. Cybern..