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… 
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References

SHOWING 1-10 OF 23 REFERENCES
Emptiness Problems for Distributed Automata
TLDR
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
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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
TLDR
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
  • H. Petersen
  • Computer Science
    Developments in Language Theory
  • 2009
TLDR
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
TLDR
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
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
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