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International Computing and Combinatorics Conference

COCOON 2007: Computing and Combinatorics pp 307–317Cite as

The Informational Content of Canonical Disjoint NP-Pairs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4598))

Abstract

We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions.

  • Q1: Where does the implication hold, and where does it fail?

  • Q2: Where can we find proof systems of different strengths, but equivalent canonical pairs?

  • Q3: What do (non-)equivalent canonical pairs tell about the corresponding proof systems?

  • Q4: Is every NP-pair (A,B), where A is NP-complete, strongly many-one equivalent to the canonical pair of some proof system?

In short, we show that both parts of Q1 and Q2 can be answered with ‘everywhere’, which generalize previous results by Pudlák and Beyersdorff. Regarding Q3, inequivalent canonical pairs tell that the proof systems are not “very similar”, while equivalent, P-inseparable canonical pairs tell that they are not “very different”. We can relate Q4 to the open problem in structural complexity that asks whether unions of disjoint NP-complete sets are NP-complete. This demonstrates a new connection between proof systems, disjoint NP-pairs, and unions of disjoint NP-complete sets.

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References

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik IV, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany

    Christian Glaßer

  2. Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY 14260,  

    Alan L. Selman & Liyu Zhang

Authors
  1. Christian Glaßer
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  2. Alan L. Selman
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  3. Liyu Zhang
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Guohui Lin

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© 2007 Springer-Verlag Berlin Heidelberg

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Glaßer, C., Selman, A.L., Zhang, L. (2007). The Informational Content of Canonical Disjoint NP-Pairs. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_31

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  • DOI: https://doi.org/10.1007/978-3-540-73545-8_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73544-1

  • Online ISBN: 978-3-540-73545-8

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