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 for infinitely many and we discuss time-space trade-offs for chain. Further we show a tight optimal space bound for the binary tree of height of the form 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.
Mots clés : reversible computations, pebbling
@article{ITA_2004__38_2_137_0,
author = {Kr\'alovi\v{c}, Richard},
title = {Time and space complexity of reversible pebbling},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {137--161},
publisher = {EDP-Sciences},
volume = {38},
number = {2},
year = {2004},
doi = {10.1051/ita:2004008},
mrnumber = {2060774},
zbl = {1082.68031},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita:2004008/}
}
TY - JOUR AU - Královič, Richard TI - Time and space complexity of reversible pebbling JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2004 SP - 137 EP - 161 VL - 38 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2004008/ DO - 10.1051/ita:2004008 LA - en ID - ITA_2004__38_2_137_0 ER -
%0 Journal Article %A Královič, Richard %T Time and space complexity of reversible pebbling %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2004 %P 137-161 %V 38 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2004008/ %R 10.1051/ita:2004008 %G en %F ITA_2004__38_2_137_0
Královič, Richard. Time and space complexity of reversible pebbling. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 2, pp. 137-161. doi : 10.1051/ita:2004008. http://archive.numdam.org/articles/10.1051/ita:2004008/
[1] , Time-space trade-offs for reversible computation. SIAM J. Comput. 18 (1989) 766-776. | MR | Zbl
[2] , and, Time and space bounds for reversible simulation, in Proc. ICALP 2001. Springer-Verlag, Lect. Notes Comput. Sci. 2076 (2001). | MR | Zbl
[3] and, A note on Bennett's time-space tradeoff for reversible computation. SIAM J. Comput. 19 (1990) 673-677. | Zbl
[4] , and, Reversible simulation of irreversible computation. Physica D 120 (1998) 168-176.
[5] and, Reversibility and adiabatic computation: trading time and space for energy. Proc. Roy. Soc. Lond. Ser. A 452 (1996) 1-21. | MR | Zbl
[6] and, Reversible simulation of irreversible computation, in Proc. 11th IEEE Conf. Computational Complexity, Philadelphia, Pennsylvania, May 24-27 (1996).
[7] and, Comparative Schematology, in MAC Conf. on Concurrent Systems and Parallel Computation (1970) 119-127.
[8] , Pebbling - The Technique for Analysing Computation Efficiency. SOFSEM'89 (1989) 205-224.
[9] and, Pebbling Dynamic Graphs in Minimal Space. RAIRO-Inf. Theor. Appl. 28 (1994) 557-565. | Numdam | MR | Zbl
[10] and, On Time-Space Trade-Offs in Dynamic Graph Pebbling. MFCS'93 711 (1993) 671-681. | Zbl
[11] , Space-Efficient Reversible Simulations. DIMACS REU report (July 2000).
[12] , On the Cost of Reversible Computations: Time-Space Bounds on Reversible Pebbling. Manuscript (1998).
Cité par Sources :
