Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Advances and applications of automata on words and trees : abstracts collection

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Advances and applications of automata on words and trees : executive summary

Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail

Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter

Suppose an observable x is the measured value (negative or non-negative) of a true mean mu (physically non-negative) in an experiment with a Gaussian resolution function with known fixed rms deviation s. The most powerful one-sided upper confidence limit at 95% C.L. is UL = x+1.64s, which I refer to as the "original diagonal line". Perceived problems in HEP with small or non-physical upper limits for x<0 historically led, for example, to substitution of max(0,x) for x, and eventually to abandonment in the Particle Data Group's Review of Particle Physics of this diagonal line relationship between UL and x. Recently Cowan, Cranmer, Gross, and Vitells (CCGV) have advocated a concept of "power constraint" that when applied to this problem yields variants of diagonal line, including UL = max(-1,x)+1.64s. Thus it is timely to consider again what is problematic about the original diagonal line, and whether or not modifications cure these defects. In a 2002 Comment, statistician Leon Jay Gleser pointed to the literature on recognizable and relevant subsets. For upper limits given by the original diagonal line, the sample space for x has recognizable relevant subsets in which the quoted 95% C.L. is known to be negatively biased (anti-conservative) by a finite amount for all values of mu. This issue is at the heart of a dispute between Jerzy Neyman and Sir Ronald Fisher over fifty years ago, the crux of which is the relevance of pre-data coverage probabilities when making post-data inferences. The literature describes illuminating connections to Bayesian statistics as well. Methods such as that advocated by CCGV have 100% unconditional coverage for certain values of mu and hence formally evade the traditional criteria for negatively biased relevant subsets; I argue that concerns remain. Comparison with frequentist intervals advocated by Feldman and Cousins also sheds light on the issues.Comment: 22 pages, 7 figure

On the logical definability of certain graph and poset languages

We show that it is equivalent, for certain sets of finite graphs, to be definable in CMS (counting monadic second-order logic, a natural extension of monadic second-order logic), and to be recognizable in an algebraic framework induced by the notion of modular decomposition of a finite graph. More precisely, we consider the set $F\_\infty$ of composition operations on graphs which occur in the modular decomposition of finite graphs. If $F$ is a subset of $F\_{\infty}$, we say that a graph is an \calF-graph if it can be decomposed using only operations in $F$. A set of $F$-graphs is recognizable if it is a union of classes in a finite-index equivalence relation which is preserved by the operations in $F$. We show that if $F$ is finite and its elements enjoy only a limited amount of commutativity -- a property which we call weak rigidity, then recognizability is equivalent to CMS-definability. This requirement is weak enough to be satisfied whenever all $F$-graphs are posets, that is, transitive dags. In particular, our result generalizes Kuske's recent result on series-parallel poset languages