Related papers: Towards Specifying Symbolic Computation
functionalObjects.h allows the C++ programmer performing common mathematical calculations to use a more symbolic syntax rather than an algorithmic syntax. This is not as ambitious as a symbolic manipulation program such as Mathematica; it…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
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…
Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space $x$ and frequency $\xi$. The symbol smoothness conditions obeyed by many…
Symbolic computation is the science of computing with symbolic objects (terms, formulae, programs, algebraic objects, geometrical objects, etc). Powerful symbolic algorithms have been developed during the past decades and have played an…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
This volume contains papers presented at the Ninth International Symposium on Symbolic Computation in Software Science, SCSS 2021. Symbolic Computation is the science of computing with symbolic objects (terms, formulae, programs,…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…
The aim of this work is to show how symbolic computation can be used to perform multivariate Lagrange, Hermite and Birkhoff interpolation and help us to build more realistic interpolating functions. After a theoretical introduction in which…