Unification in datastructure multisets
Journal of Automated Reasoning
Theory of linear and integer programming
Theory of linear and integer programming
Journal of Automated Reasoning
An algebraic approach to unification under associativity and commutativity
Journal of Symbolic Computation
Associative-commutative unification
Journal of Symbolic Computation
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
Compatibility of Systems of Linear Constraints over the Set of Natural Numbers
Cybernetics and Systems Analysis
Single Elementary Associative-Commutative Matching
Journal of Automated Reasoning
On the Complexity of Counting the Hilbert Basis of a Linear Diophnatine System
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
On the Complexity of Recognizing the Hilbert Basis of a Linear Diophantine System
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Criteria of Satisfiability for Homogeneous Systems of Linear Diophantine Constraints
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithms of Solution of Systems of Linear Diophantine Constraints over the Set {0,1}
Cybernetics and Systems Analysis
Proceedings of the 14th ACM Great Lakes symposium on VLSI
Truly heterogeneous modeling with systemC
Formal methods and models for system design
Standard bases for local rings of branches and their modules of differentials
Journal of Symbolic Computation
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Theoretical Computer Science
Algorithms for solution of systems of linear diophantine equations in residue fields
Cybernetics and Systems Analysis
Journal of Symbolic Computation
Analytic classification of plane branches up to multiplicity 4
Journal of Symbolic Computation
A note on solving linear Diophantine systems by using L3-reduction algorithm
International Journal of Computer Mathematics
Showing the non-existence of solutions in systems of linear Diophantine equations
Mathematics and Computers in Simulation
Cybernetics and Systems Analysis
Algorithms for the implementation of the analytic classification of plane branches
Journal of Symbolic Computation
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This paper presents a new method for finding complete information about the set of all nonnegative integer solutions of homogeneous and inhomogeneous linear diophantine equations. Such solutions are fundamental for associative-commutative unification. Our algorithm finds all minimal solutions as ''monotone'' paths in a graph which encodes the linear diophantine equation. This encoding makes repeated arithmetic operations obsolete and allows inexpensive tests for minimality of solutions. This graph algorithm compares favourably with the known methods, namely lexicogragraphic algorithm and completion procedure. A PASCAL implementation can be found in the Appendix.