TY - GEN

T1 - Simulating quadratic dynamical systems is PSPACE-complete (preliminary version)

AU - Arora, Sanjeev

AU - Rabani, Yuval

AU - Vazirani, Umesh

N1 - Funding Information:
*Supported by an IBM Graduate Fellowship and partly under NSF grant CCR-9310214. Email:
Funding Information:
arora~cs. berkeley. edu. ‘Work done while at ICSI, Berkeley, in part by a Rothschild postdoctoral fellowship. rabaniOtheory. lcs. nit. edu. ‘Supported by NSF grant vaziraniQcs .berkeley. edu.
Publisher Copyright:
© 1994 ACM.

PY - 1994/5/23

Y1 - 1994/5/23

N2 - Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widelyused class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS'S by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS'S is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS'S with very simple initial distributions, thus suggesting that QDS'S are intrinsically more complicated than Markov chains.

AB - Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widelyused class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS'S by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS'S is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS'S with very simple initial distributions, thus suggesting that QDS'S are intrinsically more complicated than Markov chains.

UR - http://www.scopus.com/inward/record.url?scp=0028098410&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028098410&partnerID=8YFLogxK

U2 - 10.1145/195058.195231

DO - 10.1145/195058.195231

M3 - Conference contribution

AN - SCOPUS:0028098410

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 459

EP - 467

BT - Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994

PB - Association for Computing Machinery

T2 - 26th Annual ACM Symposium on Theory of Computing, STOC 1994

Y2 - 23 May 1994 through 25 May 1994

ER -