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Complexity of cover - preserving embeddings of bipartite orders into boolean lattices

Herman G.

Reports on Mathematical Logic

2014

Vol. 49

99--117

We study the problem of deciding, whether a given partial order is embeddable into two consecutive layers of a Boolean lattice. Employing an equivalent condition for such em- beddability similar to the one given by J. Mittas and K. Reuter [5], we prove that the decision problem is NP-complete by showing a polynomial-time reduction from the not-all-equal variant of the Satisfiability problem.

Algorithms and reductions for rewriting problems

Verma R.M., Rusinowitch M., Lugiez D.

Fundamenta Informaticae

2001

Vol. 46, nr 3

257-276

In this paper we initiate a study of polynomial-time reductions for some basic decision problems of rewrite systems. We then give a polynomial-time algorithm for the unique-normal-form property of ground systems for the first time. Next we prove undecidability of several problems for a fixed string rewriting system using our reductions. Finally, we prove the decidability of confluence for commutative semi-thue systems. The Confluence and Unique-normal-form property are shown Expspace-hard for commutative semi-thue systems. We also show that there is a family of string rewrite systems for which the word problem is trivially decidable but confluence is undecidable, and we show a linear equational theory with decidable word problem but undecidable linear equational matching problem.