# On the Shuffle Automaton Size for Words

@article{Biegler2010OnTS, title={On the Shuffle Automaton Size for Words}, author={Franziska Biegler and Mark Daley and Ian McQuillan}, journal={J. Autom. Lang. Comb.}, year={2010}, volume={15}, pages={53-70} }

We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v which ensure a quadratic upper bound on the state size of u shuffled with v. Moreover, switching only two letters within one of u or v is enough to trigger the change from quadratic to exponential.

## 9 Citations

### On Comparing Deterministic Finite Automata and the Shuffle of Words

- Computer ScienceCIAA
- 2014

This paper provides a polynomial time algorithm to decide whether the language accepted by a deterministic finite automaton is a subset of the shuffle of two words, for the special case when the skeletons of the two words are of fixed length.

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## References

SHOWING 1-10 OF 10 REFERENCES

### Tight Lower Bound for the State Complexity of Shuffle of Regular Languages

- Computer ScienceJ. Autom. Lang. Comb.
- 2002

It is proved that this bound can be reached for some (not necessarily complete) deterministic finite automata with, respectively, m and n states.

### An Introduction to Automata Theory

- Computer Science
- 1988

Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines Parallel and serial…

### Introduction to Automata Theory, Languages and Computation

- Computer Science
- 1979

### Shuffle Quotient and Decompositions

- Mathematics, Computer ScienceDevelopments in Language Theory
- 2001

A right congruence relation is introduced that is the analogy of the Nerode Congruence when catenation is replaced by shuffle that shows that for certain subclasses of regular languages the shuffle decomposition problem is decidable.

### NFA to DFA Transformation for Finite Languages over Arbitrary Alphabets

- Computer ScienceJ. Autom. Lang. Comb.
- 1997

### Regular Languages

- MathematicsHandbook of Formal Languages
- 1997

The class of regular sets is the smallest class of sets containing the finite sets which is closed under union, concatenation, and Kleene closure and any finite set can be very easily generated by a regular grammar.

### Tight Lower Bound for the State Complexity of Shuffle of Regul ar Languages

- J. of Autom., Lang., and Comb
- 2002