Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Theorem-proving with resolution and superposition
Journal of Symbolic Computation
Term rewriting and all that
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Reasoning About Recursively Defined Data Structures
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Journal of Automated Reasoning
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Nelson-Oppen, shostak and the extended canonizer: a family picture with a newborn
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
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We consider the problem of efficiently building extended canonizers, which are capable of solving the uniform word problem for some first-order theories. These reasoning artifacts have been introduced in previous work to solve the lack of modularity of Shostak combination schema while retaining its efficiency. It is known that extended canonizers can be modularly combined to solve the uniform word problem in unions of theories. Unfortunately, little is known about efficiently implementing such canonizers for component theories, especially those of interest for verification like, e.g., those of uninterpreted function symbols or lists. In this paper, we investigate this problem by adapting and combining work on rewriting-based decision procedures for satisfiability in first-order theories and SER graphs, a graph-based method defined for abstract congruence closure. Our goal is to build graph-based extended canonizers for theories which are relevant for verification. Based on graphs our approach addresses implementation issues that were lacking in previous rewriting-based decision procedure approaches and which are important to argue the viability of extended canonizers.