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Can we infer sources of errors from outputs of the complex data analytics software? Bidirectional programming promises that we can reverse flow of software, and translate corrections of output into corrections of either input or data…

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…

Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a…

We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…

Forgetting - or variable elimination - is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have…

In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…

Tree ensembles, including boosting methods, are highly effective and widely used for tabular data. However, large ensembles lack interpretability and require longer inference times. We introduce a method to prune a tree ensemble into a…

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…

Dynamic arrays, also referred to as vectors, are fundamental data structures used in many programs. Modeling their semantics efficiently is crucial when reasoning about such programs. The theory of arrays is widely supported but is not…

Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…

The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…

We present a control design procedure for nonlinear control systems in which we represent a potentially high dimensional system with a low dimensional continuous-state abstraction. The abstraction generates a reference which the original…

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…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

Automatic data abstraction is an important capability for both benchmarking machine intelligence and supporting summarization applications. In the former one asks whether a machine can `understand' enough about the meaning of input data to…

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or…

An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…

Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs…

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…