# Time and space complexity of reversible pebbling

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 38, Issue: 2, page 137-161
- ISSN: 0988-3754

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topKrálovič, Richard. "Time and space complexity of reversible pebbling." RAIRO - Theoretical Informatics and Applications 38.2 (2010): 137-161. <http://eudml.org/doc/92736>.

@article{Královič2010,

abstract = {
This paper investigates one possible model of reversible computations, an
important paradigm in the context of quantum computing. Introduced by
Bennett, a reversible pebble game is an
abstraction of reversible computation that allows to examine the space and
time complexity of various classes of problems. We present a technique
for proving lower and upper bounds on time and space complexity for several
types of graphs. Using this technique we show that the time needed to
achieve optimal space for chain topology is Ω(nlgn) for infinitely
many n and we discuss
time-space trade-offs for chain. Further we show a tight optimal
space bound for the binary tree of height h of the form h + Θ(lg*h)
and discuss space complexity for the butterfly. These results give an
evidence that reversible computations need more resources than standard
computations. We also show an upper bound on time and space complexity of
the reversible pebble game based on the time and space complexity of the
standard pebble game, regardless of the topology of the graph.
},

author = {Královič, Richard},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Reversible computations; pebbling.; quantum computing},

language = {eng},

month = {3},

number = {2},

pages = {137-161},

publisher = {EDP Sciences},

title = {Time and space complexity of reversible pebbling},

url = {http://eudml.org/doc/92736},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Královič, Richard

TI - Time and space complexity of reversible pebbling

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 2

SP - 137

EP - 161

AB -
This paper investigates one possible model of reversible computations, an
important paradigm in the context of quantum computing. Introduced by
Bennett, a reversible pebble game is an
abstraction of reversible computation that allows to examine the space and
time complexity of various classes of problems. We present a technique
for proving lower and upper bounds on time and space complexity for several
types of graphs. Using this technique we show that the time needed to
achieve optimal space for chain topology is Ω(nlgn) for infinitely
many n and we discuss
time-space trade-offs for chain. Further we show a tight optimal
space bound for the binary tree of height h of the form h + Θ(lg*h)
and discuss space complexity for the butterfly. These results give an
evidence that reversible computations need more resources than standard
computations. We also show an upper bound on time and space complexity of
the reversible pebble game based on the time and space complexity of the
standard pebble game, regardless of the topology of the graph.

LA - eng

KW - Reversible computations; pebbling.; quantum computing

UR - http://eudml.org/doc/92736

ER -

## References

top- C.H. Bennett, Time-space trade-offs for reversible computation. SIAM J. Comput.18 (1989) 766-776. Zbl0676.68010
- H. Buhrman, J. Tromp and P. Vitányi, Time and space bounds for reversible simulation, in Proc. ICALP 2001. Springer-Verlag, Lect. Notes Comput. Sci.2076 (2001). Zbl0988.81021
- R.Y. Levine and A.T. Sherman, A note on Bennett's time-space tradeoff for reversible computation. SIAM J. Comput.19 (1990) 673-677. Zbl0697.68043
- M. Li, J. Tromp and P.M.B. Vitányi, Reversible simulation of irreversible computation. Physica D120 (1998) 168-176.
- M. Li and P.M.B. Vitányi, Reversibility and adiabatic computation: trading time and space for energy. Proc. Roy. Soc. Lond. Ser. A452 (1996) 1-21. Zbl0869.68019
- M. Li and P.M.B. Vitányi, Reversible simulation of irreversible computation, in Proc. 11th IEEE Conf. Computational Complexity, Philadelphia, Pennsylvania, May 24-27 (1996).
- M.S. Paterson and C.E. Hewitt, Comparative Schematology, in MAC Conf. on Concurrent Systems and Parallel Computation (1970) 119-127.
- P. Ružička, Pebbling – The Technique for Analysing Computation Efficiency. SOFSEM'89 (1989) 205-224.
- P. Ružička and J. Waczulík, Pebbling Dynamic Graphs in Minimal Space. RAIRO-Inf. Theor. Appl.28 (1994) 557-565. Zbl0884.68096
- P. Ružička and J. Waczulík, On Time-Space Trade-Offs in Dynamic Graph Pebbling. MFCS'93711 (1993) 671-681. Zbl0925.68153
- R. Williams, Space-Efficient Reversible Simulations. DIMACS REU report (July 2000).
- A. Zavarský, On the Cost of Reversible Computations: Time-Space Bounds on Reversible Pebbling. Manuscript (1998).

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