Related papers: Unification modulo a 2-sorted Equational theory fo…
In the recently emerging field of nonabelian group-based cryptography, a prominently used one-way function is the Conjugacy Search Problem (CSP), and two important classes of platform groups are polycyclic and matrix groups. In this paper,…
In this paper, we show a new tagging scheme for cryptographic protocol messages. Under this tagging, equational theories of operators such as exclusive-or, binary addition etc. are effectively disabled, when terms are unified. We believe…
We present an optimal method for encoding cluster assignments of arbitrary data sets. Our method, Random Cycle Coding (RCC), encodes data sequentially and sends assignment information as cycles of the permutation defined by the order of…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase…
This paper discusses the application of known techniques, knowledge and technology in a novel way for encryption. Two distinct and separate methods are presented. Method 1: Alter the symbol set of the language by adding additional redundant…
We present a decoder for nonbinary CWS quantum codes using the structure of union codes. The decoder runs in two steps: first we use a union of stabilizer codes to detect a sequence of errors, and second we build a new code, called union…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
An ensemble method should cleverly combine a group of base classifiers to yield an improved classifier. The majority vote is an example of a methodology used to combine classifiers in an ensemble method. In this paper, we propose to combine…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing…
With the rise of generative paradigms, generative recommendation has garnered increasing attention. The core component is the item code, generally derived by quantizing collaborative or semantic representations to serve as candidate items…
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…
A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is…
A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the…
In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the convergence analysis for such methods has been obtained in an…
Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. Equational unification is of special relevance to automated deduction, theorem…
Three candidate approaches for univariate sumcheck over roots of unity are presented. The first takes the form of a multilinear evaluation protocol, which can be combined with the standard multivariate sumcheck protocol. The other two are…
We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify…