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On binary constraint problems
The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski, and a class of examples over a fixed finite algebra on which all iterative local algorithms, whether parallel or sequential, must take quadratic time is given. Expand
Some varieties containing relation algebras
Three varieties of algebras are introduced which extend the variety RA of relation algebras. They are obtained from RA by weakening the associative law for relative product, and are consequentlyExpand
Nonfinite Axiomatizability Results for Cylindric and Relation Algebras
  • R. Maddux
  • Computer Science, Mathematics
  • J. Symb. Log.
  • 1 September 1989
The main tools are a construction of nonrepresentable one-generated relationAlgebras, a method for obtaining cylindric algebrAs from relation algeBRas, and the use of relation alGEbras in defining algebraic semantics for first-order logic. Expand
On binary constraint networks
This work forms networks and algorithms in a general algebraic setting, that of Tarski’s relation algebra, and obtains a parallel O(n logn) upper bound for path-consistency, and considers BCNs over various classes of relations that arise from an underlying linearly ordered set. Expand
Relation algebra reducts of cylindric algebras and an application to proof theory
For every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language ℒ with equality and exactly one nonlogical binary relation symbol E, such that X contains only 3 variables, and X has a proof containing exactly α + 1 variables, but X has no proof containing only α variables. Expand
Relation Algebras
  • R. Maddux
  • Computer Science
  • Relational Methods in Computer Science
  • 1997
1 2. Binary relations 4 3. Complement and converse 5 4. Union and intersection 6 5. Relative multiplication and addition 7 6.
A sequent calculus for relation algebras
  • R. Maddux
  • Computer Science, Mathematics
  • Ann. Pure Appl. Log.
  • 1 October 1983
Algebres finies et resultats d'independance, modeles canoniques, le calcul sequent algebrique. Expand
Finitary Algebraic Logic
  • R. Maddux
  • Computer Science, Mathematics
  • Math. Log. Q.
  • 1989
The equational theory of CA 3 is undecidable
There is no algorithm for determining whether or not an equation is true in every 3-dimensional cylindric algebra. This theorem completes the solution to the problem of finding those values of a andExpand
The Equational Theory of CA3 is Undecidable