Related papers: Expressiveness and Extensions of an Instruction Se…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Most scripting languages nowadays use regex pattern-matching libraries. These regex libraries borrow the syntax of regular expressions, but have an informal semantics that is different from the semantics of regular expressions, removing the…
We present an algebraic semantics for governed execution in which governance is axiomatized, compositional, and coterminous with expressibility. The framework, mechanized in 32 Rocq modules (~12,000 lines, 454 theorems, 0 admitted), is…
A rigid loop is a for-loop with a counter not accessible to the loop body or any other part of a program. Special instructions for rigid loops are introduced on top of the syntax of the program algebra PGA. Two different semantic…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
What symbolic format should an LLM emit for reliable 3D scene editing from natural language, and does algebraic structure help beyond compact syntax? We evaluate Conformal Geometric Algebra (CGA) as a compact symbolic interface against a…
The representation zeta function of a profinite group $G$ encodes the distribution of continuous irreducible complex representations of $G$ as a function of the dimension. Its abscissa of convergence $\alpha(G)$ describes the polynomial…
Single-pass instruction sequences under execution are considered to produce behaviours to be controlled by some execution environment. Threads as considered in thread algebra model such behaviours: upon each action performed by a thread, a…
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…
We study several aspects of the behaviours produced by instruction sequences under execution in the setting of the algebraic theory of processes known as ACP. We use ACP to describe the behaviours produced by instruction sequences under…
A parameterized algebraic theory of instruction sequences, objects that represent the behaviours produced by instruction sequences under execution, and objects that represent the behaviours exhibited by the components of the execution…
Exploiting the power of pre-trained models, prompt-based approaches stand out compared to other continual learning solutions in effectively preventing catastrophic forgetting, even with very few learnable parameters and without the need for…
In this article we propose feature graph architectures (FGA), which are deep learning systems employing a structured initialisation and training method based on a feature graph which facilitates improved generalisation performance compared…
Let us consider a linear control system \Sigma on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object S to \Sigma which…
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…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump…
Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
Graph reasoning agents operating from natural-language inputs must solve a coupled problem: they must reconstruct a structured graph instance from text, decide whether existing computational assets are sufficient, interact with tools under…