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).
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Fürer, M. (1984). The computational complexity of the unconstrained limited domino problem (with implications for logical decision problems). In: Börger, E., Hasenjaeger, G., Rödding, D. (eds) Logic and Machines: Decision Problems and Complexity. LaM 1983. Lecture Notes in Computer Science, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13331-3_48
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DOI: https://doi.org/10.1007/3-540-13331-3_48
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