The complexity of linear problems in fields
Journal of Symbolic Computation
Automatic recognition of tractability in inference relations
Journal of the ACM (JACM)
A shorter model theory
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Automated complexity analysis based on ordered resolution
Journal of the ACM (JACM)
Polynomial-time computation via local inference relations
ACM Transactions on Computational Logic (TOCL)
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Hierarchical and Modular Reasoning in Complex Theories: The Case of Local Theory Extensions
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
On local reasoning in verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Data structure specifications via local equality axioms
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Hierarchic reasoning in local theory extensions
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Hierarchical reasoning for the verification of parametric systems
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Automatic verification of real-time systems with rich data: an overview
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Hierarchical reasoning and model generation for the verification of parametric hybrid systems
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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In this paper we study theory combinations over non-disjoint signatures in which hierarchical and modular reasoning is possible. We use a notion of locality of a theory extension parameterized by a closure operator on ground terms. We give criteria for recognizing these types of theory extensions. We then show that combinations of extensions of theories which are local in this extended sense also have a locality property and hence allow modular and hierarchical reasoning. We thus obtain parameterized decidability and complexity results for many (combinations of) theories important in verification.