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Surjunctive Groups
This chapter is devoted to surjunctivity of maps, groups, dynamical systems, and subshifts. It includes a study of minimal subshifts, almost periodic...
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Residually Finite Groups
This chapter is mainly devoted to residual finiteness of groups, monoids, and rings, and to the Hopf property for groups. It includes a discussion of...
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Cellular Automata
This chapter introduces configuration spaces over general groups, their subshifts, and the cellular automata between them. Finiteness properties for...
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Cellular Automata
In this chapter we introduce the notion of a cellular automaton. We fix a group and an arbitrary set which will be called the alphabet. A...
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Amenable Groups
This chapter is devoted to the class of amenable groups. This is a class of groups which plays an important role in many areas of mathematics such as...
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Linear Cellular Automata
In this chapter we study linear cellular automata, namely cellular automata whose alphabet is a vector space and which are linear with respect to the...
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Amenable Groups
This chapter is devoted to group amenability. It includes a detailed study of nilpotent groups, polycyclic groups, and solvable groups.
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Local Embeddability and Sofic Groups
This chapter is devoted to local embeddability of groups, LEF-groups and LEA-groups in the sense of Vershik and Gordon, and sofic groups in the sense...
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Linear Cellular Automata
This chapter is devoted to linear cellular automata and their group ring matricial representations. This includes the study of linear surjunctivity...
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Finitely Generated Groups
The growth functions of various finitely generated groups are studied. A proof of the Nielsen-Schreier theorem on subgroups of free groups and of the...
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Surjunctive Groups
Surjunctive groups are defined in Sect. 3.1 as being the groups on which all injective cellular automata with finite alphabet are surjective. In...
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The Garden of Eden Theorem
The Garden of Eden Theorem gives a necessary and sufficient condition for the surjectivity of a cellular automaton with finite alphabet over an...
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Local Embeddability and Sofic Groups
In this chapter we study the notions of local embeddability and soficity for groups. Roughly speaking, a group is locally embeddable into a given...
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The Garden of Eden Theorem
This chapter is devoted to the Garden of Eden theorem and some of its generalizations. The homoclinicity relation for a dynamical system is...
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Residually Finite Groups
This chapter is devoted to the study of residually finite groups, which form a class of groups of special importance in several branches of...
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Finitely Generated Groups
This chapter is devoted to the growth and amenability of finitely generated groups. The choice of a finite symmetric generating subset for a finitely...
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A Tale of Optimizing the Space Taken by de Bruijn Graphs
In the last decade in bioinformatics, many computational works have studied a graph data structure used to represent genomic data, the de Bruijn...
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On False Heine/Borel Compactness Principles in Proof Mining
The use of certain false Heine/Borel compactness principles is justified in source theories of proof mining. The justification rests on the...
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Dedekind Cuts and Long Strings of Zeros in Base Expansions
In this paper, we study the complexity of irrational numbers under different representations. It is well-known that they can be computably...
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Complexity and Categoricity of Injection Structures Induced by Finite State Transducers
An injection structure \({\mathcal A}= (A,f)\)...