Related papers: Descriptive Complexity of $\#\textrm{AC}^0$ Functi…
Multiclass classification (MCC) is a fundamental machine learning problem of classifying each instance into one of a predefined set of classes. In the deep learning era, extensive efforts have been spent on developing more powerful neural…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
Program decomposition is essential for developing maintainable and efficient software, yet it remains a challenging skill to teach and learn in introductory programming courses. What does program decomposition for procedural CS1 programs…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…
We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs,…
An important objective of research in counting complexity is to understand which counting problems are approximable. In this quest, the complexity class TotP, a hard subclass of #P, is of key importance, as it contains self-reducible…
We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
Famous descriptive characterisations of P and PSPACE are restated in terms of the Cook-Nguyen style second order bounded arithmetic. We introduce an axiom of inductive definitions over second order bounded arithmetic. We show that P can be…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We describe and motivate a proposed new approach to lowerbounding the circuit complexity of boolean functions, based on a new formalization of "patterns" as elements of a special basis of the vector space of all truth table properties. We…