Proceedings ArticleDOI
Taking it to the limit: on infinite variants of NP-complete problems
Tirza Hirst,David Harel +1 more
- pp 292-304
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The work was motivated by trying to understand what makes some NP problems highly undecidable in the infinite case, while others remain on low levels of the arithmetical hierarchy.Abstract:
Infinite, recursive versions of NP optimization problems are defined. For example, MAX CLIQUE becomes the question of whether a recursive graph contains an infinite clique. The work was motivated by trying to understand what makes some NP problems highly undecidable in the infinite case, while others remain on low levels of the arithmetical hierarchy. Two results are proved; one enables using knowledge about the infinite case to yield implications to the finite case, and the other enables implications in the other direction. Taken together, the two results provide a method for proving (finitary) problems to be outside the syntactic class MAX NP, hence outside MAX SNP too. The technique is illustrated with many examples. >read more
Citations
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Some natural decision problems in automatic graphs
Dietrich Kuske,Markus Lohrey +1 more
TL;DR: These problems of existence of a Hamiltonian path and existence of an infinite path in a tree are equally complex for automatic and for recursive graphs (-complete), but are much simpler for automatic than for recursion graphs (decidable and -complete, resp.).
Posted Content
Approximation Algorithms for PSPACE-Hard Hierarchically and Periodically Specified Problems
TL;DR: The results provide the first examples of natural PSPACE-hard optimization problems that have polynomial time approximation schemes, and several of the problems considered are PSPace-hard.
Proceedings ArticleDOI
Completeness results for recursive data bases
Tirza Hirst,David Harel +1 more
TL;DR: This work defines two query languages, one for each of these possibilities, and proves their completeness, and addresses the related notion of BP-completeness.
A Survey of Recursive Combinatorics
TL;DR: In this article, it is shown that it is hard to tell if a homogeneous set is a recursive set, and the problem of detecting if a set is recursive is NP-hard.
Journal ArticleDOI
Approximation Algorithms for PSPACE-Hard Hierarchically and Periodically Specified Problems
TL;DR: In this paper, the first polynomial time approximation schemes for PSPACE-hard hierarchically or periodically specified problems were presented. But these schemes are restricted to planar instances and cannot be used for general graphs.
References
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Journal ArticleDOI
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.
Journal ArticleDOI
Optimization, approximation, and complexity classes
TL;DR: It follows that such a complete problem has a polynomial-time approximation scheme iff the whole class does, and that a number of common optimization problems are complete for MAX SNP under a kind of careful transformation that preserves approximability.
Proceedings ArticleDOI
Proof verification and hardness of approximation problems
TL;DR: Agarwal et al. as discussed by the authors showed that the MAXSNP-hard problem does not have polynomial-time approximation schemes unless P=NP, and for some epsilon > 0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup 1/ε / unless P = NP.
Journal ArticleDOI
Theory of Recursive Functions and Effective Computability
TL;DR: If searching for the ebook by Hartley Rogers Theory of Recursive Functions and Effective Computability in pdf format, then you've come to the faithful site, which presented the complete version of this book in PDF, DjVu, doc, ePub, txt forms.