相关论文: Parallel Identity Testing for Skew Circuits with B…
In this paper we study arithmetic computations in the nonassociative, and noncommutative free polynomial ring $\mathbb{F}\{x_1,x_2,\ldots,x_n\}$. Prior to this work, nonassociative arithmetic computation was considered by Hrubes, Wigderson,…
Hrube\v{s} and Wigderson [HW14] initiated the study of noncommutative arithmetic circuits with division computing a noncommutative rational function in the free skew field, and raised the question of rational identity testing. It is now…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Static alias analysis of different type of programming languages has been drawing researcher attention. However most of the results of existing techniques for alias analysis are not precise enough compared to needs of modern compilers.…
With phenomenal growth of high speed and complex computing applications, the design of low power and high speed logic circuits have created tremendous interest. Conventional computing devices are based on irreversible logic and further…
The utility of domain-specific knowledge for modeling, simulation, and optimization has been demonstrated for various research problem domains, including power systems. The concept of Equivalent Circuit Programming was previously developed…
A major problem in using iterative number generators of the form x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Motivated by the fundamental lower bounds questions in proof complexity, we initiate the study of matrix identities as hard instances for strong proof systems. A matrix identity of $d \times d$ matrices over a field $\mathbb{F}$, is a…
We observe that a certain kind of algebraic proof - which covers essentially all known algebraic circuit lower bounds to date - cannot be used to prove lower bounds against VP if and only if what we call succinct hitting sets exist for VP.…
We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short…
Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
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…
Computational asymmetry, i.e., the discrepancy between the complexity of transformations and the complexity of their inverses, is at the core of one-way transformations. We introduce a computational asymmetry function that measures the…
Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link…
Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study…
Recently a powerful class of rate-compatible serially concatenated convolutional codes (SCCCs) have been proposed based on minimizing analytical upper bounds on the error probability in the error floor region. Here this class of codes is…