1 Cellular automata over shifts and subshifts: Garden of Eden theorems and surjunctivity
-
Tullio Ceccherini-Silberstein
Abstract
This is a survey discussing some recent developments in the theory of cellular automata over shifts and subshifts on groups. The alphabet may be finite or infinite. In the infinite alphabet case, we consider linear cellular automata as well as algebraic cellular automata. We discuss various versions of the Garden of Eden theorem and results related to surjunctivity and Kaplansky conjectures.
Abstract
This is a survey discussing some recent developments in the theory of cellular automata over shifts and subshifts on groups. The alphabet may be finite or infinite. In the infinite alphabet case, we consider linear cellular automata as well as algebraic cellular automata. We discuss various versions of the Garden of Eden theorem and results related to surjunctivity and Kaplansky conjectures.
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- List of Contributing Authors VII
- 1 Cellular automata over shifts and subshifts: Garden of Eden theorems and surjunctivity 1
- 2 Languages, groups, and equations 63
- 3 Stallings’ automata 95
- 4 Groups with multiple context-free word problems 161
- 5 Parallel complexity in group theory 183
- 6 The word problem for automaton groups 265
- Index 397
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- List of Contributing Authors VII
- 1 Cellular automata over shifts and subshifts: Garden of Eden theorems and surjunctivity 1
- 2 Languages, groups, and equations 63
- 3 Stallings’ automata 95
- 4 Groups with multiple context-free word problems 161
- 5 Parallel complexity in group theory 183
- 6 The word problem for automaton groups 265
- Index 397
