The computational complexity of the unconstrained limited domino problem (with implications for logical decision problems)

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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 (cn) nondeterministic time lower bound (upper bound O(dn)). As a consequence, the non-deterministic time complexity of the decision problem for the Вε ВВ class of predicate calculus lies between Θ (cn/log n) and O(dn/log n).

Original languageEnglish (US)
Title of host publicationLogic and Machines
Subtitle of host publicationDecision Problems and Complexity - Proceedings of the Symposium Rekursive Kombinatorik
EditorsE. Borger, G. Hasenjaeger, D. Rodding
PublisherSpringer Verlag
Pages312-319
Number of pages8
ISBN (Print)9783540133315
DOIs
Publication statusPublished - Jan 1 1984
EventSymposium on Rekursive Kombinatorik, 1983 - Munster, Germany
Duration: May 23 1983May 28 1983

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume171 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherSymposium on Rekursive Kombinatorik, 1983
CountryGermany
CityMunster
Period5/23/835/28/83

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Furer, M. (1984). The computational complexity of the unconstrained limited domino problem (with implications for logical decision problems). In E. Borger, G. Hasenjaeger, & D. Rodding (Eds.), 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