A regular language is called union-free if it can be represented by a regular expression that does not contain the union operation. Every regular language can be decomposed into a union of a finite number of union-free languages (the so-called union-free decomposition). We call the number of components in the minimal union-free decomposition of a regular language the union width of the regular ...

We show that there exists a Turing degree which is minimal and fixed point free.

It is useful to discuss what parameters of supersymmetric models are presently constrained or unconstrained by experiment and to delineate the various schemes that exist for reducing the set of free parameters to a manageable number. The information presented here is derived from discussions between Paolo Gondolo and Rick Gaitskell, Vuk Mandic, and myself. The parameters fixed by experiment are...

We begin the chapter with some history of the results that form the background of this book. We then define higher matrix factorizations, our main focus. While classical matrix factorizations were factorizations of a single element, higher matrix factorizations deal directly with sequences of elements. In section 1.3, we outline our main results. Throughout the book, we use the notation introdu...

We investigate the class of context-free insertion-deletion systems. It is known that such systems are universal if the length of the inserted/deleted string is at least three. We show that if this length is bounded to two, then the obtained systems are not universal. We characterise the obtained class and we introduce a new complexity measure for insertion-deletion systems, which permits a bet...

We present a simple and efficient algorithm to solve deletefree planning problems optimally and calculate the h+ heuristic. The algorithm efficiently computes a minimum-cost hitting set for a complete set of disjunctive action landmarks generated on the fly. Unlike other recent approaches, the landmarks it generates are guaranteed to be set-inclusion minimal. In almost all delete-relaxed IPC do...

Due to the potentially immense amount of frequent sets that can be generated from transactional databases, recent studies have demonstrated the need for concise representations of all frequent sets. These studies resulted in several successful algorithms that only generate a lossless subset of the frequent sets. In this paper, we present a unifying framework encapsulating most known concise rep...

A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the smallest triangle-free 6-chromatic graphs have at least 32 and at most 40 vertices. We also determine the complete set of all triangle-free 5-chromatic graphs up to 23 vertices and all triangle-free 5-chromatic graphs on 24 vertices with maximum degree at most 7. This implies that Reed’s conject...

In recent years, two different multigraded variants of Castelnuovo-Mumford regularity have been developed, namely multigraded regularity, defined by the vanishing of multigraded pieces of local cohomology modules, and the resolution regularity vector, defined by the multi-degrees in a minimal free resolution. In this paper, we study the relationship between multigraded regularity and the resolu...

This paper describes a deep-parsing approach to SemEval-2014 Task 6, a novel context-informed supervised parsing and semantic analysis problem in a controlled domain. The system comprises a handbuilt rule-based solution based on a preexisting broad coverage deep grammar of English, backed up by a off-the-shelf datadriven PCFG parser, and achieves the best score reported among the task participa...