The computational complexity of distance functions of two-dimensional domains

Authors:
Arthur W. Chou;Ker-I Ko
Affiliations:
Department of Mathematics and Computer Science, Clark University, Worcester, MA;Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY
Venue:
Theoretical Computer Science
Year:
2005

Citing 4
Cited 1

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Complexity theory of real functions
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Abstract

We study the computational complexity of the distance function associated with a polynomial-time computable two-dimensional domains, in the context of the Turing machine-based complexity theory of real functions. It is proved that the distance function is not necessarily computable even if a two-dimensional domain is polynomial-time recognizable. On the other hand, if both the domain and its complement are strongly polynomial-time recognizable, then the distance function is polynomial-time computable if and only if P = NP.