Related papers: Variant-based Equational Unification under Constru…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that…
Comparison and evaluation of graph-based representations of sentence meaning is a challenge because competing representations of the same sentence may have different number of nodes, and it is not obvious which nodes should be compared to…
For small number of equations, systems of linear (and sometimes nonlinear) equations can be solved by simple classical techniques. However, for large number of systems of linear (or nonlinear) equations, solutions using classical method…
The symbol is used to describe the Springer correspondence for the classical groups. We propose equivalent definitions of symbols for rigid partitions in the $B_n$, $C_n$, and $D_n$ theories uniformly. Analysing the new definition of symbol…
We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…
A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
Asymmetric unification, or unification with irreducibility constraints, is a newly developed paradigm that arose out of the automated analysis of cryptographic protocols. However, there are still relatively few asymmetric unification…
Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…
Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite…
Visual Question Answering (VQA) has emerged as a Visual Turing Test to validate the reasoning ability of AI agents. The pivot to existing VQA models is the joint embedding that is learned by combining the visual features from an image and…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
This short note presents some variant schemes of boundary variation diminishing (BVD) algorithm in one dimension with the results of numerical tests for linear advection equation to facilitate practical use. In spite of being presented in…
The resolvability of equations in integers containing truncated Newton's binomial, is determined by the divisibility of the binomial by the characteristic parameters of the equation, which most often is the binomial exponent. Two types of…
Computer-aided analysis of security protocols heavily relies on equational theories to model cryptographic primitives. Most automated verifiers for security protocols focus on equational theories that satisfy the Finite Variant Property…
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…
The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…
We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…