Related papers: Hypercomputation, Frege, Deleuze: Solving Thomson'…
Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…
In the article 'Ordinal Logics and the Characterizations of the Informal Concept of Proof', Georg Kreisel poses the problem of assigning unique notations to recursive ordinals, and additionally suggests that the methods which are developed…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
Hyperproperties, like observational determinism or symmetry, cannot be expressed as properties of individual computation traces, because they describe a relation between multiple computation traces. HyperLTL is a temporal logic that…
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…
The paper presents a solution to the long-standing question about the decidability of the two-variable fragment of the superintuitionistic predicate logic $\mathbf{QLC}$ defined by the class of linear Kripke frames, which is also the…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…
If the same neuron activates for both "lender" and "riverside," standard metrics attribute the overlap to superposition--the neuron must be compressing two unrelated concepts. This work explores how much of the overlap is due a lexical…
Complementarity problems often permit distinct solutions, a fact of major significance in optimization, game theory and other fields. In this paper, we develop a numerical technique for computing multiple isolated solutions of…
Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…
The halting problem is considered to be an essential part of the theoretical background to computing. That halting is not in general computable has supposedly been proved in many text books and taught on many computer science courses, in…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…
Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the…
The usual $\epsilon,\delta$-definition of the limit of a function (whether presented at a rigorous or an intuitive level) requires a "candidate $L$" for the limit value. Thus, we have to start our first calculus course with "guessing"…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…