## Abstract

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.

Original language | American English |
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Title of host publication | Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994 |

Publisher | Association for Computing Machinery |

Pages | 459-467 |

Number of pages | 9 |

ISBN (Electronic) | 0897916638 |

DOIs | |

State | Published - 23 May 1994 |

Externally published | Yes |

Event | 26th Annual ACM Symposium on Theory of Computing, STOC 1994 - Montreal, Canada Duration: 23 May 1994 → 25 May 1994 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F129502 |

ISSN (Print) | 0737-8017 |

### Conference

Conference | 26th Annual ACM Symposium on Theory of Computing, STOC 1994 |
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Country/Territory | Canada |

City | Montreal |

Period | 23/05/94 → 25/05/94 |

### Bibliographical note

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.