Automatic recognition of tractability in inference relations
Journal of the ACM (JACM)
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Information and Computation - Special issue: Combining logical systems
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Hierarchical and Modular Reasoning in Complex Theories: The Case of Local Theory Extensions
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Deciding Extensions of the Theories of Vectors and Bags
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Incremental Instance Generation in Local Reasoning
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
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CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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Constraint solving for interpolation
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Invariant synthesis for combined theories
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Verifying CSP-OZ-DC specifications with complex data types and timing parameters
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
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
Automatic verification of parametric specifications with complex topologies
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Towards complete reasoning about axiomatic specifications
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Decision procedures for automating termination proofs
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Proceedings of the 14th international conference on Hybrid systems: computation and control
An efficient decision procedure for imperative tree data structures
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Journal of Automated Reasoning
Interpolation in local theory extensions
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Constraint solving for program verification: theory and practice by example
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Combining data structures with nonstably infinite theories using many-sorted logic
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
A decision procedure for monotone functions over bounded and complete lattices
TARSKI'02-05 Proceedings of the 2006 international conference on Theory and Applications of Relational Structures as Knowledge Instruments - Volume 2
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Hierarchical reasoning for the verification of parametric systems
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Deciding functional lists with sublist sets
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Complete instantiation-based interpolation
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Instantiation Schemes for Nested Theories
ACM Transactions on Computational Logic (TOCL)
Hierarchical reasoning and model generation for the verification of parametric hybrid systems
CADE'13 Proceedings of the 24th international conference on Automated Deduction
Automating separation logic using SMT
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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We show that for special types of extensions of a base theory, which we call local, efficient hierarchic reasoning is possible. We identify situations in which it is possible, for an extension $\mathcal{T}_{1}$ of a theory $\mathcal{T}_{0}$, to express the decidability and complexity of the universal theory of $\mathcal{T}_{1}$ in terms of the decidability resp. complexity of suitable fragments of the theory $\mathcal{T}_{0}$ (universal or ∀∃). These results apply to theories related to data types, but also to certain theories of functions from mathematics.