3 citations · 8 across the 12 of their papers we have counts for
12 papers
An Algebra of Properties of Binary Relations
Jochen Burghardt
We consider all 16 unary operations that, given a homogeneous binary relation R, define a new one by a boolean combination of xRy and yRx. Operations can be composed, and connected…
Simple Laws about Nonprominent Properties of Binary Relations
Jochen Burghardt
We checked each binary relation on a 5-element set for a given set of properties, including usual ones like asymmetry and less known ones like Euclideanness. Using a poor man's Qui…
A Scheme-Driven Approach to Learning Programs from Input/Output Equations
Jochen Burghardt
We describe an approach to learn, in a term-rewriting setting, function definitions from input/output equations. By confining ourselves to structurally recursive definitions we obt…
An Improved Algorithm for E-Generalization
Jochen Burghardt
E-generalization computes common generalizations of given ground terms w.r.t. a given equational background theory E. In 2005 [arXiv:1403.8118], we had presented a computation appr…
Weight Computation of Regular Tree Languages
Jochen Burghardt
We present a general framework to define an application-dependent weight measure on terms that subsumes e.g. total simplification orderings, and an O(n log n) algorithm for the sim…
Repetition-Free Derivability from a Regular Grammar is NP-Hard
Jochen Burghardt
We prove the NP-hardness of the problem whether a given word can be derived from a given regular grammar without repeated occurrence of any nonterminal.
Experiences in Developing Time-Critical Systems - The Case Study "Production Cell"
Jochen Burghardt
Starting from an informal requirements description of a toy production cell used in an intra-project competition in 1994, we give a formal specification that is as close as possibl…
Implementing Anti-Unification Modulo Equational Theory
Jochen Burghardt, Birgit Heinz
We present an implementation of E-anti-unification as defined in Heinz (1995), where tree-grammar descriptions of equivalence classes of terms are used to compute generalizations m…
Regular Substitution Sets: A Means of Controlling E-Unification
Jochen Burghardt
A method for selecting solution constructors in narrowing is presented. The method is based on a sort discipline that describes regular sets of ground constructor terms as sorts. I…
Axiomatization of Finite Algebras
Jochen Burghardt
We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a…
E-Generalization Using Grammars
Jochen Burghardt
We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization set…
Maintaining partial sums in logarithmic time
Jochen Burghardt
We present a data structure that allows to maintain in logarithmic time all partial sums of elements of a linear array during incremental changes of element's values.