• Corpus ID: 118583850

# Time-space tradeoffs for two-way finite automata

@article{Zheng2015TimespaceTF,
title={Time-space tradeoffs for two-way finite automata},
author={Shenggen Zheng and Daowen Qiu and Jozef Gruska},
journal={arXiv: Quantum Physics},
year={2015}
}
• Published 6 July 2015
• Computer Science
• arXiv: Quantum Physics
We explore bounds of {\em time-space tradeoffs} in language recognition on {\em two-way finite automata} for some special languages. We prove: (1) a time-space tradeoff upper bound for recognition of the languages $L_{EQ}(n)$ on {\em two-way probabilistic finite automata} (2PFA): $TS={\bf O}(n\log n)$, whereas a time-space tradeoff lower bound on {\em two-way deterministic finite automata} is ${\bf \Omega}(n^2)$, (2) a time-space tradeoff upper bound for recognition of the languages $L_{INT}(n… 2 Citations ## Figures from this paper Lower Bound and Hierarchies for Quantum Ordered Read-k-times Branching Programs • Mathematics, Computer Science ArXiv • 2017 Lower bound for quantum$k$-OBDD is got for quantum version of known computational model Ordered Read-times Branching Programs or Ordered Binary Decision Diagrams with repeated test for k=o(\sqrt{n})$.
Lower Bounds and Hierarchies for Quantum Memoryless Communication Protocols and Quantum Ordered Binary Decision Diagrams with Repeated Test
• Computer Science
SOFSEM
• 2018
This work explores multi-round quantum memoryless communication protocols that mean that players forget history from previous rounds, and their behavior is obtained only by input and message from the opposite player, and presents a lower bound for Quantum Ordered Read-k-times Branching Programs (k-QOBDD).

## References

SHOWING 1-10 OF 35 REFERENCES
Two-way finite automata with quantum and classical state
• Computer Science
Theor. Comput. Sci.
• 2002
One-Way Finite Automata with Quantum and Classical States
• Computer Science
Languages Alive
• 2012
It is proved that coin-tossing one-way probabilistic finite automata (coin-Tossing 1PFA) and one- way quantum finite Automata with control language (1QFACL) as well as several other models of QFA, can be simulated by 1QCFA.
Succinctness of two-way probabilistic and quantum finite automata
• Computer Science
Discret. Math. Theor. Comput. Sci.
• 2010
It is proved that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions, and two- way nondeterministic finite automaton (2NFAs), and it is shown that 2ZFAs with mixed states can support highly efficient probability amplification.
• Computer Science
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
• 1998
We obtain the first non-trivial time-space tradeoff lower bound for functions f: {0,1}/sup n//spl rarr/{0,1} on general branching programs by exhibiting a Boolean function f that requires exponential
1-way quantum finite automata: strengths, weaknesses and generalizations
• Computer Science
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
• 1998
This work constructs a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton, and thinks that this construction may be useful for design of other space-efficient quantum algorithms.
On the state complexity of semi-quantum finite automata
• Computer Science
RAIRO Theor. Informatics Appl.
• 2014
Three results of such a type that are stronger in some sense than other ones because they deal with models of quantum finite automata with very little quantumness so-called semi-quantum one- and two-way finite Automata.
Generalizations of the distributed Deutsch–Jozsa promise problem
• Mathematics, Computer Science
Mathematical Structures in Computer Science
• 2015
This paper generalizes the above distributed Deutsch–Jozsa promise problem to determine, for any fixed $\frac{n}{2}$⩽ k ⩽ n, whether H(x, y) = 0 or H( x, y), and shows that an exponential gap between exact quantum and deterministic communication complexity still holds.