# 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} }

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…

## 64 Citations

### Linear grammars with one-sided contexts and their automaton representation

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2014

The main result is the undecidability of the emptiness problem for grammars restricted to a one-symbol alphabet, which is proved by simulating a Turing machine by a cellular automaton with feedback.

### On LL(k) linear conjunctive grammars

- Computer ScienceArXiv
- 2021

This paper investigates the LL(k) subclass of linear conjunctive grammars, defined by analogy with the classical LL( k) Grammars: these are grammar that admit top-down linear-time parsing with k-symbol lookahead, and a parser for these grammARS that works in linear time and uses logarithmic space is constructed.

### Comparing Linear Conjunctive Languages to Subfamilies of the Context-Free Languages

- Computer ScienceSOFSEM
- 2011

This paper investigates subclasses of the context-free languages for possible containment in this class and shows that every visibly pushdown automaton can be simulated by a one-way real-time cellular automaton, but already for LL(1) context- free languages and for one-counter DPDAs no simulation is possible.

### Input-driven languages are linear conjunctive

- Computer Science, LinguisticsTheor. Comput. Sci.
- 2016

### Boolean Grammars

- Computer ScienceDevelopments in Language Theory
- 2003

A new class of formal grammars, which allow the use of all set-theoretic operations as an integral part of the formalism of rules, are introduced, which allows to conjecture the practical applicability of the new concept.

### Defining Contexts in Context-Free Grammars

- Computer ScienceLATA
- 2012

This paper gives two equivalent definitions of the model and establishes its basic properties, including a transformation to a normal form, a cubic-time parsing algorithm, and another recognition algorithm working in linear space.

### Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth

- Computer ScienceTheory of Computing Systems
- 2008

The results imply undecidability of a number of decision problems of unary conjunctive grammars, as well as non-existence of a recursive function bounding the growth rate of the generated languages.

### Underlying Principles and Recurring Ideas of Formal Grammars

- Computer ScienceLATA
- 2018

The paper investigates some of the fundamental ideas of the context-free grammar theory, as they are applied to several extensions and subclasses of context- Free Grammar, including multi-component grammars, tree-adjoining grammARS, conjunctivegrammars and Boolean Grammars.

### Linear Conjunctive Grammars and One-turn Synchronized Alternating Pushdown Automata

- Computer ScienceInt. J. Found. Comput. Sci.
- 2009

A subfamily of synchronized alternating pushdown automata is introduced, one-turn synchronized alternating Pushdown Automata, which accept the same class of languages as those generated by linear conjunctive grammars, thus strengthening the claim of synchronised alternating push down automata as a natural counterpart of conj unctive Grammars.

## References

SHOWING 1-10 OF 17 REFERENCES

### Whale calf, a parser generator for conjunctive grammars

- Computer ScienceCIAA'02
- 2002

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

- Computer ScienceProgramming and Computer Software
- 2004

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

- Computer ScienceJ. Comput. Syst. Sci.
- 1972

### Cellular Automata and Formal Languages

- Computer ScienceSWAT
- 1970

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

- Computer Science, LinguisticsHandbook of Formal Languages
- 1997

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

- Computer ScienceSIAM J. Comput.
- 1985

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).

### Characterizations and Computational Complexity of Systolic Trellis Automata

- Computer ScienceTheor. Comput. Sci.
- 1984

### On real-time cellular automata and trellis automata

- Computer ScienceActa Informatica
- 2004

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

- Computer Science
- 1984

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.