https://www.ibisc.univ-evry.fr/~hutzler/Cours/IMBI_MPS/Kari05.pdf

Theory of cellular automata: a survey

A senior undergraduate or graduate level computer science textbook on algorithm design for distributed computer systems.

/pdf/an-introduction-to-distributed-algorithms-2scptn142v.pdf

An Introduction to Distributed Algorithms

Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the present day. The emphasis is mainly on topics closer to computer science and mathematics rather than physics, biology or other applications. The work should be of interest to both new entrants into the field as well as researchers working on particular aspects of cellular automata.

http://krchowdhary.com/me-tfl/0-a%20brief%20history%20of%20cellular%20automata.pdf

A brief history of cellular automata

Three self-stabilizing protocols for distributed systems in the shared memory model are presented The first protocol is a mutual-exclusion protocol for tree structured systems The second protocol is a spanning tree protocol for systems with any connected communication graph The third protocol is obtained by use of fair protocol combination, a simple technique which enables the combination of two self-stabilizing dynamic protocols The result protocol is a self-stabilizing, mutual-exclusion protocol for dynamic systems with a general (connected) communication graph The presented protocols improve upon previous protocols in two ways: First, it is assumed that the only atomic operations are either read or write to the shared memory Second, our protocols work for any connected network and even for dynamic networks, in which the topology of the network may change during the execution

https://link.springer.com/content/pdf/10.1007/BF02278851.pdf

Self-stabilization of dynamic systems assuming only read/write atomicity

The first self-stabilizing end-to-end communication protocol and the most efficient known self-stabilizing network reset protocol are introduced. A simple method of local checking and correction, by which distributed protocols can be made self-stabilizing without the use of unbounded counters, is used. The self-stabilization model distinguishes between catastrophic faults that abstract arbitrary corruption of global state, and other restricted kinds of anticipated faults. It is assumed that after the execution starts there are no further catastrophic faults, but the anticipated faults may continue to occur. >

Self-stabilization by local checking and correction

A self-stabilizing system has the property that, no matter how it is perturbed, it eventually returns to a legitimate configuration. Dijkstra originally introduced the self-stabilization problem and gave several solutions for a ring of processors in his 1974 Communications of the ACM paper. His solutions use a distinguished processor in the ring, which effectively acts as a controlling element to drive the system toward stability. Dijkstra has observed that a distinguished processor is essential if the number of processors in the ring is composite. We show, by presenting a protocol and proving its correctness, that there is a self-stabilizing system with no distinguished processor if the size of the ring is prime. The basic protocol uses T (n2) states in each processor when n is the size of the ring. We modify the basic protocol to obtain one that uses T (n2/ln n) states.

Uniform self-stabilizing rings

The limit sets of cellular automata, defined by Wolfram, play an important role in applications of cellular automata to complex systems. A number of results on limit sets are proved, considering both finite and infinite configurations of cellular automata. The main concern of this paper is with testing membership and (essential) emptiness of limit sets for linear and two-dimensional cellular automata.

On the limit sets of cellular automata

A self-stabilizing system has the property that it eventually reaches a legitimate configuration when started in any arbitrary configuration. Dijkstra originally introduced the self-stabilization problem and gave several solutions for a ring of processors [Dij74]. His solutions, and others that have appeared, use a distinguished processor in the ring, which can help to drive the system toward stability. Dijkstra observed that a distinguished processor is essential if the number of processors in the ring is composite [Dij82]. We show that there is a self-stabilizing system with no distinguished processor if the size of the ring is prime. Our basic protocol use Θ(n2) states in each processor, where n is the size of the ring. We also give a refined protocol which uses only Θ(n2/ln n) states.

A lower bound for probabilistic distributed algorithms

This paper is concerned with sets of infinite strings (ω-languages) and mappings between them. The main result is that there is an algorithm for testing the (string by string) equality of two homomorphisms on an ω-regular set of infinite strings. As a corollary we show that it is decidable whether two functional finite-state transducers define the same function on infinite strings (are ω-equivalent).

Jan K. Pachl

Papers

Uniform self-stabilizing rings

On the limit sets of cellular automata

Uniform self-stabilizing rings

A lower bound for probabilistic distributed algorithms

Equivalence problems for mappings on infinite strings