### Abstract

The unconstrained domino or tiling problem is the following. Given a finite set T (of tiles), sets H,V ⊑ T×T and a cardinal k ≤ ω, does there exist a function:k×k->T such that (t(i,j),t(i+1,j))εH and (t(i,j),t(i,j+1))εV for all i,j<k ? The unlimited domino problem (k infinite) has played an important role in the process of finding the undecidability proof for the ∀ε∀ prefix class of predicate calculus. The limited domino problem is similarly connected to some decidable prefix classes. The limited domino problem is NP-complete, if k is given in unary. The same was conjectured for k given in binary, but we show an Θ (c^{n}) nondeterministic time lower bound (upper bound O(d^{n})). As a consequence, the non-deterministic time complexity of the decision problem for the Вε ВВ class of predicate calculus lies between Θ (c^{n/log n}) and O(d^{n/log n}).

Original language | English (US) |
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Title of host publication | Logic and Machines |

Subtitle of host publication | Decision Problems and Complexity - Proceedings of the Symposium Rekursive Kombinatorik |

Editors | E. Borger, G. Hasenjaeger, D. Rodding |

Publisher | Springer Verlag |

Pages | 312-319 |

Number of pages | 8 |

ISBN (Print) | 9783540133315 |

DOIs | |

Publication status | Published - Jan 1 1984 |

Event | Symposium on Rekursive Kombinatorik, 1983 - Munster, Germany Duration: May 23 1983 → May 28 1983 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 171 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Symposium on Rekursive Kombinatorik, 1983 |
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Country | Germany |

City | Munster |

Period | 5/23/83 → 5/28/83 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Logic and Machines: Decision Problems and Complexity - Proceedings of the Symposium Rekursive Kombinatorik*(pp. 312-319). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 171 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-13331-3_48