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Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional…
The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Complementation of finite automata is a basic operation used in numerous applications. The standard way to complement a nondeterministic finite automaton (NFA) is to transform it into an equivalent deterministic finite automaton (DFA) and…
We present a finite-state, deterministic automaton that emulates the Collatz function through digitwise transitions on base-10 representations. Each digit is represented as a symbolic triplet (r, p, c) encoding its value, the parity of the…
Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A…
A mimic computing oriented automaton can directly portray the behaviors of a mimic computing system. In this paper, we investigate the following theoretical problems on this type of automata: operational semantics and computational ability.…
The processing and analysis of computed tomography (CT) imaging is important for both basic scientific development and clinical applications. In AutoCT, we provide a comprehensive pipeline that integrates an end-to-end automatic…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
Point cloud is one of the widely used techniques for representing and storing 3D geometric data. In the past several methods have been proposed for processing point clouds. Methods such as PointNet and FoldingNet have shown promising…
Finitary Idealized Concurrent Algol (FICA) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of FICA, which in principle can be used to prove…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
Encodings, that is, injective functions from words to words, have been studied extensively in several settings. In computability theory the notion of encoding is crucial for defining computability on arbitrary domains, as well as for…
A \emph{data automaton} is a finite automaton equipped with variables (counters or registers) ranging over infinite data domains. A trace of a data automaton is an alternating sequence of alphabet symbols and values taken by the counters…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
Both performance and efficiency are important to semantic segmentation. State-of-the-art semantic segmentation algorithms are mostly based on dilated Fully Convolutional Networks (dilatedFCN), which adopt dilated convolutions in the…
Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…