On the equivalence of linear conjunctive grammars and trellis automata

@article{Okhotin2004OnTE,
  title={On the equivalence of linear conjunctive grammars and trellis automata},
  author={Alexander Okhotin},
  journal={RAIRO Theor. Informatics Appl.},
  year={2004},
  volume={38},
  pages={69-88}
}
  • A. Okhotin
  • Published 2004
  • Computer Science
  • RAIRO Theor. Informatics Appl.
This paper establishes computational equivalence of two seemingly unrelated concepts: linear conjunctive grammars and trellis automata. Trellis automata, also studied under the name of one-way real-time cellular automata, have been known since early 1980s as a purely abstract model of parallel computers, while linear conjunctive grammars, introduced a few years ago, are linear context-free grammars extended with an explicit intersection operation. Their equivalence implies the equivalence of… 
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References

SHOWING 1-10 OF 17 REFERENCES

Whale calf, a parser generator for conjunctive grammars

Whale Calf is a parser generator that uses conjunctive grammars, a generalization of context-free grammars with an explicit intersection operation, as the formalism of specifying the language. All…

Conjunctive Grammars and Systems of Language Equations

  • A. Okhotin
  • Computer Science
    Programming and Computer Software
  • 2004
TLDR
Every system of this kind of language equations that are resolved with respect to variables and contain the operations of concatenation, union and intersection is proved to have a least fixed point, and the equivalence of these systems to conjunctive grammars is established.

Real-Time Language Recognition by One-Dimensional Cellular Automata

Cellular Automata and Formal Languages

TLDR
Many positive results are presented to indicate that the context-free languages can, perhaps, be accepted in time n and space n by cellular automata.

Context-Free Languages and Pushdown Automata

TLDR
This chapter is devoted to context-free languages, which were designed initially to formalize grammatical properties of natural languages and grammars and appeared to be well adapted to the formal description of the syntax of programming languages.

Sequential Machine Characterizations of Trellis and Cellular Automata and Applications

TLDR
It is shown that a new speed-up theorem is proved which is stronger than what has previously been shown and presented, for the first time, sequential machine characterizations of TA’s (CA”s).

The Algebraic Theory of Context-Free Languages*

Characterizations and Computational Complexity of Systolic Trellis Automata

On real-time cellular automata and trellis automata

SummaryIt is shown that f(n)-time one-way cellular automata are equivalent to f(n)-time trellis automata, the real-time one-way cellular automata languages are closed under reversal, the 2n-time…

Systolic trellis automatat

TLDR
Theoretical results e.g. the closure of (homogeneous) systolic automaton under Boolean operations, or that every linear context free language can be accepted by a homogeneous systolics automaton and that their languages have time complexity 0(n2) are derived.