Related papers: On the Lattice of Program Metrics
Argumentation is a formalism allowing to reason with contradictory information by modeling arguments and their interactions. There are now an increasing number of gradual semantics and impact measures that have emerged to facilitate the…
We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric…
This paper studies the quantitative refinements of Abramsky's applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $\lambda$-calculus with a linear type system that can express programs…
In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
We introduce the $L_!^S$-calculus, a linear lambda-calculus extended with scalar multiplication and term addition, that acts as a proof language for intuitionistic linear logic (ILL). These algebraic operations enable the direct expression…
We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…
Software developers and maintainers need to read and understand source programs and other software artifacts. The increase in size and complexity of software drastically affects several quality attributes, especially understandability and…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values over multiple examples, such as intervals. To overcome this limitation, we introduce an inductive…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
Embedding data into vector spaces is a very popular strategy of pattern recognition methods. When distances between embeddings are quantized, performance metrics become ambiguous. In this paper, we present an analysis of the ambiguity…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce $\textit{space}$ efficiencies, the price being $\textit{time}$ performances often poorer than those…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…
The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language (NL) statements into First-Order Logic~(FOL) and external theorem provers.…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…