In order to find a causal explanation for data presented in the form of covariance and con­ centration matrices it is necessary to decide if the graph formed by such associations is a projection of a directed acyclic graph ( dag). We show that the general problem of deciding whether such a dag exists is NP-complete.

NP-complete problems should be hard on some instances but these may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a graph coloring problem: this graph problem is hard on average unless all NP problem under any samplable (i.e. generateable in polynomial time) distribution a...

The system design process translates the customers’ needs into a buildable system design. It requires selecting subsystems from an allowable set and matching the interfaces between them. Designs that meet the top-level input and output requirements are tested to see how well they meet the system’s performance and cost goals. This paper proves that the System Design Problem is NP-complete by red...

One of the central questions in topology is determining whether a given curve is knotted or unknotted. An algorithm to decide this question was given by Haken in 1961, using the technique of normal surfaces. These surfaces are rigid, discretized surfaces, well suited for algorithmic analysis. Any oriented surface without boundary can be obtained from a sphere by adding “handles”. The number of ...

We focus on automated revision techniques for adding Unity properties to distributed programs. We show that unlike centralized programs where multiple safety properties and one progress property can be added in polynomial-time, addition of a safety or a progress Unity property to distributed programs is significantly more difficult. Precisely, we show that such addition is NP-complete in the si...

The Maze Generation problem has been presented as a benchmark for the Second Answer Set Programming Competition. We prove that the problem is NP–complete and identify relevant classes of unsatisfiable instances. The Maze Generation (MG) problem has been presented as a benchmark for the Second Answer Set Programming (ASP) Competition1. The problem has been placed in the NP category, which contai...

In 1925, the German physicist Ernst Ising introduced a simple mathematical model of phase transitions, the abrupt changes of state that occur, for example, when water freezes or a cooling lump of iron becomes magnetic. In the 75 years since, the Ising model has been analyzed, generalized, and computerized—but never, except in special cases, solved. Researchers managed to get exact answers for p...

In this paper we prove that the derivability problems for productfree Lambek calculus and product-free Lambek calculus allowing empty premises are NP-complete. Also we introduce a new derivability characterization for these calculi.

During the last years, the genomes of more and more species have been sequenced, providing data for phylogenetic reconstruction based on genome rearrangement measures, where the most important distance measures are the reversal distance and the transposition distance. The two main tasks in all phylogenetic reconstruction algorithms is to calculate pairwise distances and to solve the median of t...