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Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
Recent work has shown that the input-output behavior of some machine learning systems can be captured symbolically using Boolean expressions or tractable Boolean circuits, which facilitates reasoning about the behavior of these systems.…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…
A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these…
Dynamic mode decomposition (DMD) is a versatile approach that enables the construction of low-order models from data. Controller design tasks based on such models require estimates and guarantees on predictive accuracy. In this work, we…
The growing interest in explainable artificial intelligence (XAI) for critical decision making motivates the need for interpretable machine learning (ML) models. In fact, due to their structure (especially with small sizes), these models…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
We present a novel stochastic approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the…
Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each…
One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively…
M\"obius inversion and Shapley values are two mathematical tools for characterizing and decomposing higher-order structure in complex systems. The former defines higher-order interactions as discrete derivatives over a partial order; the…
In this paper I demonstrate a novel design for an optoelectronic State Machine which replaces input/output forming logic found in conventional state machines with BDD based optical logic while still using solid state memory in the form of…
We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing…
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and…
Covariate-shift generalization, a typical case in out-of-distribution (OOD) generalization, requires a good performance on the unknown test distribution, which varies from the accessible training distribution in the form of covariate shift.…
A key operation in processing an unbounded data stream is windowing, which extracts finite portions of streams for further handling. The existing frameworks and query languages either require windows to be defined using ad hoc imperative…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
The growing demand for oriented object detection (OOD) across various domains has driven significant research in this area. However, the high cost of dataset annotation remains a major concern. Current mainstream OOD algorithms can be…