Modal logics, description logics and arithmetic reasoning
Artificial Intelligence
Complexity Results for First-Order Two-Variable Logic with Counting
SIAM Journal on Computing
Programming by Refinement, as Exemplified by the SETL Representation Sublanguage
ACM Transactions on Programming Languages and Systems (TOPLAS)
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Information and Computation
Spectra of Monadic Second-Order Formulas with One Unary Function
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Complexity of the Two-Variable Fragment with Counting Quantifiers
Journal of Logic, Language and Information
Weakest-precondition of unstructured programs
PASTE '05 Proceedings of the 6th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
Deciding Boolean Algebra with Presburger Arithmetic
Journal of Automated Reasoning
Modular Pluggable Analyses for Data Structure Consistency
IEEE Transactions on Software Engineering
The software model checker Blast: Applications to software engineering
International Journal on Software Tools for Technology Transfer (STTT)
Full functional verification of linked data structures
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Towards Efficient Satisfiability Checking for Boolean Algebra with Presburger Arithmetic
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Regional Logic for Local Reasoning about Global Invariants
ECOOP '08 Proceedings of the 22nd European conference on Object-Oriented Programming
A combination framework for tracking partition sizes
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Cardinality Abstraction for Declarative Networking Applications
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
VCC: A Practical System for Verifying Concurrent C
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Decision Procedures for Set-Valued Fields
Electronic Notes in Theoretical Computer Science (ENTCS)
Decision procedures for multisets with cardinality constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Combining theories with shared set operations
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Carathéodory bounds for integer cones
Operations Research Letters
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Ordered sets in the calculus of data structures
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Sets with cardinality constraints in satisfiability modulo theories
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Proceedings of the 33rd International Conference on Software Engineering
Decision procedures for region logic
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Deciding functional lists with sublist sets
VSTTE'12 Proceedings of the 4th international conference on Verified Software: theories, tools, experiments
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Logics that involve collections (sets, multisets), and cardinality constraints are useful for reasoning about unbounded data structures and concurrent processes. To make such logics more useful in verification this paper extends them with the ability to compute direct and inverse relation and function images. We establish decidability and complexity bounds for the extended logics.