Related papers: A composition theorem for decision tree complexity
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
A key requirement on any well-behaved process language is its compositionality: behavioural equivalence of processes should be respected by the constructors of the language. Turi and Plotkin's abstract GSOS provides an elegant bialgebraic…
This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$,…
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
We report on a method for compiling decision trees into weighted finite-state transducers. The key assumptions are that the tree predictions specify how to rewrite symbols from an input string, and the decision at each tree node is…
For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group $M^*/M$. This gives a wealth of conformal data, which we realize…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new…
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…
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
We report on work towards flexible algorithms for solving decision problems represented as influence diagrams. An algorithm is given to construct a tree structure for each decision node in an influence diagram. Each tree represents a…
The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in $[0,1]$,…