# Counter Machines and Distributed Automata: A Story about Exchanging Space and Time

@inproceedings{Carton2018CounterMA, title={Counter Machines and Distributed Automata: A Story about Exchanging Space and Time}, author={Olivier Carton and Bruno Guillon and Fabian Reiter}, booktitle={Automata}, year={2018} }

We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of counters. The two classes differ in the extra features they offer: one allows to copy counter values, whereas the other allows to compute copyless sums of counters. Our distributed automata, on the other hand, operate on directed path graphs that represent words…

## 7 Citations

Emptiness problems for distributed automata

- Computer ScienceInf. Comput.
- 2020

The decidability of the emptiness problem for three classes of distributed automata is investigated and a characterization of constraint satisfaction problems is provided by identifying a class of automata with exactly the same computational power.

Freezing, Bounded-Change and Convergent Cellular Automata

- Computer Science, MathematicsArXiv
- 2019

It is shown that all settings can achieve universality in the sense of Blondel-Delvenne-Kurka, although short term predictability varies from NLOGSPACE to P-complete, and the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension 1.

The Mirage of Universality in Cellular Automata

- Computer Science, MathematicsArXiv
- 2021

It is shown how some cellular automata can embed efficient but bounded computation, while others can embed unbounded computations but not efficiently, and two variants of Boolean circuit embedding, transient versus repeatable simulations, and underline their differences.

Iterative arrays with finite inter-cell communication

- Computer Science
- 2020

It can be shown that all such decidability questions remain undecidable even if only four communications per cell are allowed, and the undecidability results are shown to hold as well for one-way and two-way cellular automata having at most fourcommunications per cell.

Iterative Arrays with Finite Inter-cell Communication

- Computer ScienceAutomata
- 2019

By reduction of Hilbert's tenth problem it can be shown that all such decidability questions remain undecidable for iterative arrays where the maximum number of communications per cell occurring in accepting computations is drastically bounded by a constant number.

Cellular Automata and Discrete Complex Systems

- Computer ScienceLecture Notes in Computer Science
- 2019

Details of Invited Talks Quantum Cellular Automata: Computability and Universality are presented, including a discussion of the role of language in the development of knowledge representation.

An intelligent agent of finite state machine in educational game “Flora the Explorer”

- Computer ScienceJournal of Physics: Conference Series
- 2019

## References

SHOWING 1-10 OF 23 REFERENCES

Emptiness Problems for Distributed Automata

- Computer ScienceGandALF
- 2017

It is shown that the emptiness problem is undecidable in LogSpace for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state.

Indirect addressing and the time relationships of some models of sequential computation

- Computer Science
- 1979

It is shown that counter machines augmented by a “copy” instruction can be simulated in linear time by counter machines without such an instruction, and that these counter machines can be simulate by RAM's with speedup by a fixed polynomial.

Asynchronous Distributed Automata: A Characterization of the Modal Mu-Fragment

- Mathematics, Computer ScienceICALP
- 2017

It is established that the equivalence on finite directed graphs between a class of asynchronous distributed automata and a small fragment of least fixpoint logic and the expressive power of these machines is independent of whether or not messages can be lost.

Descriptional Complexity of Cellular Automata and Decidability Questions

- Mathematics, Computer ScienceDCFS
- 2001

It is proved that the language class accepted by realtime-OCA is incomparable to many known and well-investigated language classes and nonrecursive trade-offs are shown to exist between certain restricted classes of cellular automata.

Counter machines and counter languages

- Computer ScienceMathematical systems theory
- 2005

The languages recognizable by time- and space-restricted multiple-counter machines are compared to the languages recognizable by similarly restricted multipletape Turing machines. Special emphasis is…

Regular Functions and Cost Register Automata

- Computer Science, Mathematics2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2013

A deterministic model for associating costs with strings that is parameterized by operations of interest, a notion of regularity that provides a yardstick to measure expressiveness, and decision problems and theoretical properties of resulting classes of cost functions are proposed.

Modal Logic and Distributed Message Passing Automata

- Mathematics, Computer ScienceCSL
- 2013

A variety of highly natural logical characterizations of classes of distributed message passing automata that run in constant time are reported, and it is established that MSC contains the Sigma^\mu_1 fragment of the modal \mu-calculus in the finite.

Simulations by Time-Bounded Counter Machines

- Computer ScienceDevelopments in Language Theory
- 2009

A simulation of a pushdown store is described which is optimal in the sense that reducing the number of counters of a simulator leads to an increase in time complexity and the lower bound also establishes a tight counter hierarchy in exponential time.

Cellular automata with sparse communication

- Computer ScienceTheor. Comput. Sci.
- 2010

It is shown that even the weakest non-trivial device in question, that is, one-way cellular automata where each two neighboring cells may communicate constantly often only, accept rather complicated languages.

Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines

- Mathematics
- 1961

The equivalence of the notions of effective computability as based (1) on formal systems (e.g., those of Post), and (2) on computing machines (e.g., those of Turing) has been shown in a number of…