Labyrinth Problems

Labyrinth-Searching Abilities of Automata

Häftad, Tyska, 2012

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I. Basic Concepts.- 1.1. Graphoids.- 1.2. R-graphoids.- 1.3. C-graphoids.- 1.4. The hierarchy of types of labyrinths.- 1.5. Automata in labyrinths.- 1.6. Normal labyrinth problems and reducibility.- 1.7. Finite automata in corridors.- 1.8. Vertex substitutions.- 1.9. Edge substitutions.- 1.10. Edge insertions.- II. Searching Algorithms.- 2.1. Pidgin Programming Language and Tarry’s algorithm.- 2.2. Face-following and edge-blocking.- 2.3. The bridge-preferring method.- 2.4. Modifications of bridge-preferring.- 2.5. Edge-blocking in normed 2D ficographs.- 2.6. Regular swinging in 20 ficographs.- 2.7. Searching by means of space-bounded Turing tapes.- 2.8. Searching all infinite connected 2D graphs.- III. Trap Constructions.- 3.1. Plane R-traps for finite automata and related types.- 3.2. Traps for halting automata.- 3.3. 2D traps for finite automata.- 3.4. Corollaries about 2D traps.- 3.5. Universal traps.- 3.6. Plane R-traps for plenary multihead automata.- 3.7. Barrages and traps for cooperating systems.- IV. Supplements and Problems.- 4.1. Automata without markers in finite labyrinths.- 4.2. Marker automata and cooperating systems in finite labyrinths.- 4.3. Automata in infinite labyrinths.- 4.4. On some other results and problems.- L. Labyrinth theory.- S. Surroundings.- Q. Quotations.- Theorems, corollaries, propositions, lemmas, programs supplements, problems, figures.- Definitions.- Symbols introduced within the text.- Some predefined symbols.