Related papers: Logical Zonotopes: A Set Representation for the Fo…
We investigate a principled approach for symbolic operation completion (SOC), a minimal task for studying symbolic reasoning. While conceptually similar to matrix completion, SOC poses a unique challenge in modeling abstract relationships…
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…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
Logical relations widely exist in human activities. Human use them for making judgement and decision according to various conditions, which are embodied in the form of \emph{if-then} rules. As an important kind of cognitive intelligence, it…
The ZX calculus is a mathematical tool to represent and analyse quantum operations by manipulating diagrams which in effect represent tensor networks. Two families of nodes of these networks are ones which commute with either Z rotations or…
In this paper we formulate combinatorial identities that give representation of positive integers as linear combination of even powers of 2 with binomial coefficients. We present side by side combinatorial as well as computer generated…
Boolean symbolic reasoning for gate-level netlists is a critical step in verification, logic and datapath synthesis, and hardware security. Specifically, reasoning datapath and adder tree in bit-blasted Boolean networks is particularly…
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
Great attention has been paid to binomial codes utilizing bosonic systems as logical qubits with error correction capabilities. However, implementing single-qubit rotation operations on binomial codes has proven challenging, requiring an…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
We define and study a new abstract domain which is a fine-grained combination of zonotopes with polyhedric domains such as the interval, octagon, linear templates or polyhedron domain. While abstract transfer functions are still rather…
The Game of Life cellular automaton is a classical example of a massively parallel collision-based computing device. The automaton exhibits mobile patterns, gliders, and generators of the mobile patterns, glider guns, in its evolution. We…
In this work, we interpret the representations of multi-object scenes in vision encoders through the lens of structured representations. Structured representations allow modeling of individual objects distinctly and their flexible use based…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
We present a theoretical result, which is based on the linear algebra theory (similar operators). The obtained theoretical results optimize the experimental technique to construct quantum computer e.g., reduces the number of steps to…
The holomorphic bootstrap attempts to classify rational conformal field theories. The straight ahead approach is hard to implement when the number of characters become large. We combine all characters of an RCFT to form a vector valued…
In functional data analysis, binary classification with one functional covariate has been extensively studied. We aim to fill in the gap of considering multivariate functional covariates in classification. In particular, we propose an…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…