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Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
Whether a robot can perform some specific task depends on several aspects, including the robot's sensors and the plans it possesses. We are interested in search algorithms that treat plans and sensor designs jointly, yielding…
Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to…
Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
Many problems in Computer Science can be abstracted to the following question: given a set of objects and rules respectively, which new objects can be produced? In the paper, we consider a succinct version of the question: given a set of…
Bayesian networks are probabilistic graphical models often used in big data analytics. The problem of exact structure learning is to find a network structure that is optimal under certain scoring criteria. The problem is known to be NP-hard…
The subset sum problem is a typical NP-complete problem that is hard to solve efficiently in time due to the intrinsic superpolynomial-scaling property. Increasing the problem size results in a vast amount of time consuming in…
Existing decision-theoretic reasoning frameworks such as decision networks use simple data structures and processes. However, decisions are often made based on complex data structures, such as social networks and protein sequences, and rich…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs,…
We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We consider the solution of the subset sum problem based on a parallel computer consisting of self-propelled biological agents moving in a nanostructured network that encodes the NP-complete task in its geometry. We develop an approximate…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…
The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…