Related papers: Characterising Complexity Classes by Inductive Def…
In this paper we provide purely model-theoretic (algebraic) characterisations for classes definable in second-order logic and for pseudo-elementary classes (including PC and PC_{\Delta} classes). Classical results of this flavour include…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive families within type theory. By elaborating an inductive definition -- a…
Probabilities of causation (PoC) are valuable concepts for explainable artificial intelligence and practical decision-making. PoC are originally defined for scalar binary variables. In this paper, we extend the concept of PoC to continuous…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
This article exemplifies a novel approach to the teaching of introductory differential calculus using the modern notion of ``infinitesimal'' as opposed to the traditional approach using the notion of ``limit''. I illustrate the power of the…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal…
We provide non-asymptotic bounds for first and higher order inclusion probabilities of the rejective sampling model with various size parameters. Further we derive bounds in the semi-definite ordering for matrices that collect (conditional)…
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial…
Implicit computational complexity is a lively area of theoretical computer science, which aims to provide machine-independent characterizations of relevant complexity classes. % for uniformity with subsequent uses >> 1960s (but feel free to…
Otto's Theorem characterises the bisimulation-invariant PTIME queries over graphs as exactly those that can be formulated in the polyadic mu-calculus, hinging on the Immerman-Vardi Theorem which characterises PTIME (over ordered structures)…
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 extend dynamic logic of propositional assignments by adding an operator of parallel composition that is inspired by separation logics. We provide an axiomatisation via reduction axioms, thereby establishing decidability. We also prove…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…
We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We estimate weighted character sums with determinants $ad-bc $ of $2\times 2$ matrices modulo a prime $p$ with entries $a,b,c,d $ varying over the interval $ [1,N]$. Our goal is to obtain nontrivial bounds for values of $N$ as small as…
This paper studies the complexity of determining whether a formula in the modal logics characterizing the nested-simulation semantics is characteristic for some process, which is equivalent to determining whether the formula is satisfiable…