PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
On the complexity of integer programming
Journal of the ACM (JACM)
Hilbert Bases, Caratheodory's Theorem and Combinatorial Optimization
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The description logic handbook: theory, implementation, and applications
Model-Theoretic Methods in Combined Constraint Satisfiability
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Journal of Automated Reasoning
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Theory of Computation (Texts in Computer Science)
Theory of Computation (Texts in Computer Science)
Deciding Boolean Algebra with Presburger Arithmetic
Journal of Automated Reasoning
Modular data structure verification
Modular data structure verification
Using first-order theorem provers in the Jahob data structure verification system
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
An algorithm for deciding BAPA: boolean algebra with presburger arithmetic
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
The expressivity of constraint query languages with boolean algebra linear cardinality constraints
ADBIS'05 Proceedings of the 9th East European conference on Advances in Databases and Information Systems
Carathéodory bounds for integer cones
Operations Research Letters
Full functional verification of linked data structures
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Fractional Collections with Cardinality Bounds, and Mixed Linear Arithmetic with Stars
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
No Syllogisms for the Numerical Syllogistic
Languages: From Formal to Natural
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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
Verification of semantic commutativity conditions and inverse operations on linked data structures
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
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
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
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Journal of Artificial Intelligence Research
Local Reasoning for Global Invariants, Part I: Region Logic
Journal of the ACM (JACM)
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Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that combines 1) Boolean algebra of sets of uninterpreted elements (BA) and 2) Presburger arithmetic (PA). BAPA can express relationships between integer variables and cardinalities of unbounded sets. In combination with other decision procedures and theorem provers, BAPA is useful for automatically verifying quantitative properties of data structures. This paper examines QFBAPA, the quantifier-free fragment of BAPA. The computational complexity of QFBAPA satisfiability was previously unknown; previous QFBAPA algorithms have non-deterministic exponential time complexity due to an explosion in the number of introduced integer variables.This paper shows, for the first time, how to avoid such exponential explosion. We present an algorithm for checking satisfiability of QFBAPA formulas by reducing them to formulas of quantifier-free PA, with only O(n log(n)) increase in formula size. We prove the correctness of our algorithm using a theorem about sparse solutions of integer linear programming problems. This is the first proof that QFBAPA satisfiability is in NP and therefore NP-complete. We implemented our algorithm in the context of the Jahob verification system. Our preliminary experiments suggest that our algorithm, although not necessarily better for proving formula unsatisfiability, is more effective in detecting formula satisfiability than previous approaches.