dc.contributor.author | Song, Renzhi | |
dc.date.accessioned | 2018-09-04 18:59:40 (GMT) | |
dc.date.available | 2018-09-04 18:59:40 (GMT) | |
dc.date.issued | 2018-09-04 | |
dc.date.submitted | 2018-08-28 | |
dc.identifier.uri | http://hdl.handle.net/10012/13723 | |
dc.description.abstract | We examine various aspects of the poset retraction problem for series-parallel posets. In particular we show that the poset retraction problem for series-parallel posets that are already solvable in polynomial time are actually also solvable in nondeterministic logarithmic space (assuming P 6= NP). We do this by showing that these series-parallel posets when expanded by constants have bounded path duality. We also give a recipe for constructing members of this special class of series-parallel poset analogous to the construction of all series-parallel posets. Piecing together results from [5],[15],[14] and [12] one can deduce that if a relational structure expanded by constants has bounded path duality then it admits SD-join operations. We directly prove the existence of SD-join operations on members of this class by providing an algorithm which constructs them. Moreover, we obtain a polynomial upper bound to the length of the sequence of these operations. This also proves that for this class of series-parallel posets, having bounded path duality when expanded by constants is equivalent to admitting SD-join operations. This equivalence is not yet known to be true for general relational structures; only the forward direction is proven. However the reverse direction is known to be true for structures that admit NU operations. Zádori has classified in [26] the class of series-parallel posets admitting an NU operation and has shown that every such poset actually admits a 5-ary NU operation. We give a recipe for constructing series-parallel posets of this class analogous to the one mentioned before. Then we show an alternative proof for Zádori's result. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | Series-Parallel | en |
dc.subject | Universal Algebra | en |
dc.subject | CSP | en |
dc.subject | Retraction | en |
dc.subject | Polymorphism | en |
dc.subject | Poset | en |
dc.title | Series-Parallel Posets and Polymorphisms | en |
dc.type | Doctoral Thesis | en |
dc.pending | false | |
uws-etd.degree.department | Pure Mathematics | en |
uws-etd.degree.discipline | Pure Mathematics | en |
uws-etd.degree.grantor | University of Waterloo | en |
uws-etd.degree | Doctor of Philosophy | en |
uws.contributor.advisor | Willard, Ross | |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.published.city | Waterloo | en |
uws.published.country | Canada | en |
uws.published.province | Ontario | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |