Related papers: A note on monadic datalog on unranked trees
In mathematical phylogenetics, the time-consistent galled trees provide a simple class of rooted binary network structures that can be used to represent a variety of different biological phenomena. We study the enumerative combinatorics of…
In this paper, we address an issue of finding explainable clusters of class-uniform data in labelled datasets. The issue falls into the domain of interpretable supervised clustering. Unlike traditional clustering, supervised clustering aims…
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
Weighted First Order Model Counting (WFOMC) is fundamental to probabilistic inference in statistical relational learning models. As WFOMC is known to be intractable in general ($\#$P-complete), logical fragments that admit polynomial time…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
We provide a logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees. This results is useful for analyzing phylogenetic mixture models. The proof depends on interpreting multisets of trees as high…
Trees -- i.e., the type of data structure known under this name -- are central to many aspects of knowledge organization. We investigate some central design choices concerning the ontological modeling of such trees. In particular, we…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
Within the field of phylogenetics there is growing interest in measures for summarising the dissimilarity, or 'incongruence', of two or more phylogenetic trees. Many of these measures are NP-hard to compute and this has stimulated a…
We solve a well known, long-standing open problem in relational databases theory, showing that the conjunctive query determinacy problem (in its "unrestricted" version) is undecidable.
The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with…
The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof…
Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference…