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For supervised classification problems involving design, control, other practical purposes, users are not only interested in finding a highly accurate classifier, but they also demand that the obtained classifier be easily interpretable.…
In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for…
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of…
In this article, we deal with propositional calculi over a signature containing the classical implication $\to$ with the rules of modus ponens and substitution. For these calculi we consider few recognizing problems such as recognizing…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
We give a definition of topological entropy for tree shifts, prove that the limit in the definition exists, and show that it dominates the topological entropy of the associated one-dimensional shift of finite type when the labeling of the…
We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\tau}(K).…
Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution…
Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
This paper proposes Transducers with Pronunciation-aware Embeddings (PET). Unlike conventional Transducers where the decoder embeddings for different tokens are trained independently, the PET model's decoder embedding incorporates shared…
In context-aware trust evaluation, using ontology tree is a popular approach to represent the relation between contexts. Usually, similarity between two contexts is computed using these trees. Therefore, the performance of trust evaluation…