# Optimal Time and Communication Solutions of Firing Squad Synchronization Problems on Square Arrays, Toruses and Rings

@inproceedings{Gruska2004OptimalTA, title={Optimal Time and Communication Solutions of Firing Squad Synchronization Problems on Square Arrays, Toruses and Rings}, author={Jozef Gruska and Salvatore La Torre and Mimmo Parente}, booktitle={Developments in Language Theory}, year={2004} }

A new solution for the Firing Squad Synchronization Problem (FSSP) on two-dimensional square arrays is presented and its correctness is demonstrated in detail. Our new solution is time as well as communication optimal (the so-called minimal time 1-bit solution). In addition, it is shown that the technique developed and the results obtained allow also to solve in optimal time & communication FSSP for several other variants of this problem on networks shaped as square grids (with four Generals…

## 23 Citations

Different time solutions for the firing squad synchronization problem on basic grid networks

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2006

This work presents several solutions to the Firing Squad Synchronization Problem on grid networks of different shapes that consider one- and two-way communication modes and constrain the quantity of information that adjacent processors can exchange at each step.

Various Solutions to the Firing Squad Synchronization Problems

- Computer ScienceArXiv
- 2005

This work presents different classes of solutions to the Firing Squad Synchronization Problem on networks of different shapes that are used as building blocks to compose new solutions for all times expressed by polynomials with nonnegative coefficients.

The firing squad synchronization problem for squares with holes

- MathematicsArXiv
- 2019

This paper introduces a variation of the firing squad synchronization problem called the FSSP for squares with k holes and shows that SH[1] has a minimal-time solution.

Minimum and non-Minimum Time Solutions to the Firing Squad Synchronization Problem

- Mathematics, Computer ScienceComputing with New Resources
- 2014

A survey on the minimum and non minimum time solutions to the Firing Squad Synchronization Problem with particular emphasis on the contribution given by Jozef Gruska is presented.

Cellular ANTomata as Engines for Highly Parallel Pattern Processing

- Computer ScienceICA3PP Workshops
- 2016

This work exposes the Cellular ANTomaton (CAnt) computing model—cellular automata enhanced with mobile FSMs (Ants)—as a highly efficient VAA for a variety of pattern-processing problems that are inspired by biocomputing applications.

Finite-State Robots in a Warehouse: Achieving Linear Parallel Speedup While Rearranging Objects

- Computer Science2013 42nd International Conference on Parallel Processing
- 2013

A variety of rearrangement problems that (teams of) FSMs can solve via algorithms that are scalable-i.e., that work in arbitrarily large meshes-and fully pipeline able-and that achieve (asymptotic) linear speedup when larger teams of FSMs are deployed are studied.

Cellular ANTomata (Extended Abstract)

- Computer Science
- 2007

This work proposes using "semi-synchronous" cellular automata as a platform for efficiently realizing ant-inspired algorithms that coor- dinate robots within a fixed, geographically constrained environment.

The Parking Problem for Finite-State Robots

- Computer ScienceJ. Graph Algorithms Appl.
- 2012

This paper studies the ability of FSMs to scalably perform a simple path-planning task called parking, within xed square meshes of arbitrary sizes, which requiresFSMs to know where they are within a mesh, specically which quadrant they reside in.

Cellular Automata: Algorithms and Applications

- Computer Science
- 2009

This dissertation develops a working key generation algorithm for a public-keycryptosystem based on reversible cellular automata originally conceived by Kari, and gives an improvement to a CA algorithm which solves a version of the convexhull problem.

Cellular ANTomata: Food-Finding and Maze-Threading

- Computer Science2008 37th International Conference on Parallel Processing
- 2008

A model for realizing ant-inspired algorithms that coordinate robots within a fixed, geographically constrained environment is proposed and illustrated, which inverts the relationship between ant-robots and the environment that they navigate: intelligence now resides in the environment rather than in the ants.

## References

SHOWING 1-10 OF 15 REFERENCES

The Firing Squad Synchronization Problem for Two-Dimensional Arrays

- MathematicsInf. Control.
- 1977

On time optimal solutions of the firing squad synchronization problem for two-dimensional paths

- Computer Science, MathematicsTheor. Comput. Sci.
- 2001

Time-Optimal Solution of the Firing-Squad-Synchronization-Problem for n-Dimensional Rectangles with the General at an Arbitrary Position

- Computer Science, MathematicsTheor. Comput. Sci.
- 1982

A Six-State Minimal Time Solution to the Firing Squad Synchronization Problem

- MathematicsTheor. Comput. Sci.
- 1987

On Optimal Solutions to the Firing Squad Synchronization Problem

- Computer ScienceTheor. Comput. Sci.
- 1996

An 8-state Minimal Time Solution to the Firing Squad Synchronization Problem

- Mathematics, Computer ScienceInf. Control.
- 1967

An Optimum Solution to the Firing Squad Synchronization Problem

- BusinessInf. Control.
- 1966

Firing Squad Synchronization Problem in Reversible Cellular Automata

- Computer ScienceTheor. Comput. Sci.
- 1996

A Synchronization Problem on 1-Bit Communication Cellular Automata

- Computer Science, MathematicsInternational Conference on Computational Science
- 2003

It is shown that there still exist several new interesting synchronization algoritms on CA1-bit although more than 40 years have passed since the development of the problem, and a generalized synchronization algorithm is proposed that operates in m + n + max on two-dimensional m × n rectangular arrays.