Related papers: Projection semantics for rigid loops
In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…
Shuffle projection is motivated by the verification of safety properties of special parameterized systems. Basic definitions and properties, especially related to alphabetic homomorphisms, are presented. The relation between iterated…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…
Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently,…
The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…
A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if…
With the recent success of pre-trained models in NLP, a significant focus was put on interpreting their representations. One of the most prominent approaches is structural probing (Hewitt and Manning, 2019), where a linear projection of…