Programming by multiset transformation
Communications of the ACM
On the complexity of integer programming
Journal of the ACM (JACM)
Automatic predicate abstraction of C programs
Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Formal System Development with KIV
FASE '00 Proceedings of the Third Internationsl Conference on Fundamental Approaches to Software Engineering: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Using Decision Procedures with a Higher-Order Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Minimal Solutions of Linear Diophantine Systems: Bounds and Algorithms
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Combining Multisets with Integers
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Theoretical Computer Science - Foundations of software science and computation structures
Modular data structure verification
Modular data structure verification
Solving Quantified Verification Conditions Using Satisfiability Modulo Theories
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Efficient E-Matching for SMT Solvers
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Towards Efficient Satisfiability Checking for Boolean Algebra with Presburger Arithmetic
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Cooperating Theorem Provers: A Case Study Combining HOL-Light and CVC Lite
Electronic Notes in Theoretical Computer Science (ENTCS)
Automated verification of shape and size properties via separation logic
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Decision procedures for multisets with cardinality constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Carathéodory bounds for integer cones
Operations Research Letters
Fractional Collections with Cardinality Bounds, and Mixed Linear Arithmetic with Stars
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Deciding Extensions of the Theories of Vectors and Bags
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
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
Decision procedures for automating termination proofs
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Communications of the ACM
Building a calculus of data structures
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Collections, cardinalities, and relations
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
MUNCH - automated reasoner for sets and multisets
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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We consider an extension of integer linear arithmetic with a "star" operator takes closure under vector addition of the solution set of a linear arithmetic subformula. We show that the satisfiability problem for this extended language remains in NP (and therefore NP-complete). Our proof uses semilinear set characterization of solutions of integer linear arithmetic formulas, as well as a generalization of a recent result on sparse solutions of integer linear programming problems. As a consequence of our result, we present worst-case optimal decision procedures for two NP-hard problems that were previously not known to be in NP. The first is the satisfiability problem for a logic of sets, multisets (bags), and cardinality constraints, which has applications in verification, interactive theorem proving, and description logics. The second is the reachability problem for a class of transition systems whose transitions increment the state vector by solutions of integer linear arithmetic formulas.