Related papers: Abstract computation over first-order structures. …
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
According to a mainstream position in contemporary cognitive science and philosophy, the use of abstract compositional concepts is both a necessary and a sufficient condition for the presence of genuine thought. In this article, we show how…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…
The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Search algorithms are often categorized by their node expansion strategy. One option is the depth-first strategy, a simple backtracking strategy that traverses the search space in the order in which successor nodes are generated. An…
The field of quantum computing is at an exciting time where we are constructing novel hardware, evaluating algorithms, and finding out what works best. As qubit technology grows and matures, we need to be ready to design and program larger…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
For the additive real BSS machines using only constants 0 and 1 and order tests we consider the corresponding Turing reducibility and characterize some semi-decidable decision problems over the reals. In order to refine, step-by-step, a…
In article the basic principles put in a basis of algorithmicallysoftware of hypercomplex number calculations, structure of a software, structure of functional subsystems are considered. The most important procedures included in subsystems…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…