Related papers: Refinement in the Tableau Synthesis Framework
An emerging branch of control theory specialises in certificate learning, concerning the specification of a desired (possibly complex) system behaviour for an autonomous or control model, which is then analytically verified by means of a…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
The notion of an equational shell is studied to involve the objects and their environment. Appropriate methods are studied as valid embeddings of refined objects. The refinement process determines the linkages between the variety of…
We propose a novel approach to program synthesis, focusing on synthesizing database queries. At a high level, our proposed algorithm takes as input a sketch with soft constraints encoding user intent, and then iteratively interacts with the…
We propose a mechanism for the vertical refinement of bigraphical reactive systems, based upon a mechanism for limiting observations and utilising the underlying categorical structure of bigraphs. We present a motivating example to…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…
Counterfactual explanations are viewed as an effective way to explain machine learning predictions. This interest is reflected by a relatively young literature with already dozens of algorithms aiming to generate such explanations. These…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
In this paper, we derive a framework to understand the effect of imperfections on the phasematching spectrum of a wide class of nonlinear systems. We show that this framework is applicable to many physical systems, such as waveguides or…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
Existing Programming-By-Example (PBE) systems often rely on simplified benchmarks that fail to capture the high structural complexity-such as deeper nesting and frequent Unions-of real-world regexes. To overcome the resulting performance…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
Currently, there is a significant amount of research being conducted in the field of artificial intelligence to improve the explainability and interpretability of deep learning models. It is found that if end-users understand the reason for…
Refinement types -- types qualified with logical predicates -- have proven effective for lightweight verification in languages like Liquid Haskell, F*, and Dafny. However, in these systems refinements are either written in a separate…
Reactive synthesis is an automatic way to translate a human intention expressed in some logic into a system of some kind. This thesis has two parts, devoted to logic and to systems. In Part I, we develop two new approaches to CTL*…
Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…