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A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…
PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…
A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…
Many real-life problems of practical importance -- spanning a wide range of applications from chip design to bioinformatics -- represent constraint satisfaction problems, where classical solvers have to rely on heuristic approximations due…
Efficiently optimizing Nondeterministic Polynomial time (NP) problems in polynomial time has profound implications in many domains. CMOS oscillator networks have been shown to be effective and efficient in approximating certain NP-hard…
We investigate the NP-Complete problem SAT and the geometry of its instances. For a particular type that we call {\it non-interlaced formulas}, we propose a polynomial time algorithm for their resolution using graphs and matrices.
Boolean satisfiability (SAT) has an extensive application domain in computer science, especially in electronic design automation applications. Circuit synthesis, optimization, and verification problems can be solved by transforming original…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
Nowadays in Quantum Computing, the implementation of quantum algorithm has created a stir since Noisy Intermediate-Scale Quantum (NISQ) devices are out in the market. Researchers are mostly interested in solving NP-complete problems with…
Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…
Plug-and-Play Priors (PnP) is one of the most widely-used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful…
We solve the sign problem in a particle-hole symmetric spin-polarized fermion model on bipartite lattices using the idea of fermion bags. The solution can be extended to a class of models at half filling but without particle-hole symmetry.…
We consider the distributed message-passing {LOCAL} model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous…