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Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…
Reconfiguration paths express sequences of successive reconfiguration operations within a component-based approach allowing dynamic reconfigurations. We use constructs from regular expressions-pin particular, alternatives-to introduce…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
The union of a collection of $n$ sets is generally expressed in terms of a characteristic (indicator) function that contains $2^{n}-1$ terms. In this article, a much simpler expression is found that requires the evaluation of $n$ terms…
This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
In this paper we show how prescritive type checking and constraint solving can be combined to increase automation during software verification. We do so by defining a type system and implementing a typechecker for {log} (read `setlog'), a…
Answer Set Programming (ASP) is a well-known problem-solving formalism in computational logic. Nowadays, ASP is used in many real world scenarios thanks to ASP solvers. Standard evaluation of ASP programs suffers from an intrinsic…
We introduce a class of rooted graphs which allows one to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs and propose a new complete…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
We address the problem of tuning word embeddings for specific use cases and domains. We propose a new method that automatically combines multiple domain-specific embeddings, selected from a wide range of pre-trained domain-specific…
The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…