Related papers: Symbolic computation with finite quandles
We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…
First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
To study embeddings of tangles in knots, we use quandle cocycle invariants. Computations are carried out for the tables of knots and tangles, to investigate which tangles may or may not embed in knots in the tables.
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we…
Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic…
Dyck paths are one of the most important objects in enumerative combinatorics, and there are many papers devoted to counting selected families of Dyck paths. Here we present two approaches for the automatic counting of many such families,…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
A quandle is an algebraic system originated in knot theory, and can be regarded as a generalization of symmetric spaces. The inner automorphism group of a quandle is defined as the group generated by the point symmetries (right…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
A parallel method for computing Boolean expressions based on the properties of finite free Boolean algebras is presented. We also show how various finite combinatorial objects can be codded in the formalism of Boolean algebras and counted…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
This paper focuses on the nominal durations of musical events (notes and rests) in a symbolic musical score, and on how to conveniently handle these in computer applications. We propose the usage of a temporal unit that is directly related…
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
A quandle is a set that has a binary operation satisfying three conditions corresponding to the Reidemeister moves. Homology theories of quandles have been developed in a way similar to group homology, and have been applied to knots and…
Quandles are self-distributive algebraic structures known as sources of strong knots invariants, but also appearing in other contexts. From any quandle, one can construct two invariants: the structure group and the second quandle homology…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…