Related papers: Declarative Combinatorics: Boolean Functions, Circ…
Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
The generation of high-fidelity synthetic data is a cornerstone of modern machine learning, yet Large Language Models (LLMs) frequently suffer from hallucinations, logical inconsistencies, and mode collapse when tasked with structured…
Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. We introduce a hypergraph-based formalism, Blocks & Bonds (B&B), that generalizes…
Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs…
Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can…
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
We introduce a novel framework, termed $\lambda$DD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD…
Decomposition of any Boolean Function BF_n of n binary inputs into an optimal inverter coupled network of Symmetric Boolean functions SF_k (k \leq n) is described. Each SF component is implemented by Threshold Logic Cells, forming a…
We propose a method for decomposing continuous-variable operations into a universal gate set, without the use of any approximations. We fully characterize a set of transformations admitting exact decompositions and describe a process for…
In the work are defined the concepts semi-canonical and canonical binary matrix. What is described is an algorithm solving the combinatorial problem for finding the semi-canonical matrices in the set \Lambda_n^k consisting of all n\times n…
We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the primary data structure. We…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
We present hash embeddings, an efficient method for representing words in a continuous vector form. A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function…
We extract verified algorithms for exact real number computation from constructive proofs. To this end we use a coinductive representation of reals as streams of binary signed digits. The main objective of this paper is the formalisation of…
This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.
Factorization method is developed for a family of discretely spiked harmonic oscillators. Two sets of intertwining and ladder operators are presented to algebraically generate eigenstates with energies isomorphic to those of the ordinary…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
Database systems incorporate an ever-growing number of functions in their kernels (a.k.a., database native functions) for scenarios like new application support and business migration. This growth causes an urgent demand for automatic…