Complexity Results for First-Order Two-Variable Logic with Counting
SIAM Journal on Computing
Undecidability Results on Two-Variable Logics
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
Complexity of Two-Variable Logic with Counting
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Two-variable logic with counting is decidable
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Decidability of reachability in vector addition systems (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Complexity of the Two-Variable Fragment with Counting Quantifiers
Journal of Logic, Language and Information
Back to the future: revisiting precise program verification using SMT solvers
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Beyond Shapes: Lists with Ordered Data
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
The General Vector Addition System Reachability Problem by Presburger Inductive Invariants
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
A Logic-Based Framework for Reasoning about Composite Data Structures
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Shape analysis of single-parent heaps
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
On the complexity of the Bernays-Schönfinkel class with datalog
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Bounded model checking of pointer programs
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
On the complexity of the Bernays-Schönfinkel class with datalog
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
An efficient decision procedure for imperative tree data structures
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Two-Variable Logic with Counting and Trees
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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The Bernays-Schönfinkel class with Datalog is a 2-variable fragment of the Bernays-Schönfinkel class extended with least fixed points expressible by certain monadic Datalog programs. It was used in a bounded model checking procedure for programs manipulating dynamically allocated pointer structures, where the bounded model checking problem was reduced to the satisfiability of formulas in this logic. The best known upper bound on the complexity of the satisfiability problem for this logic was 2NEXPTIME. In this paper we extend the Bernays-Schönfinkel class with Datalog to a more expressive logic -- a fragment of two-variable logic with counting quantifiers extended with the same kind of fixed points. We prove that both satisfiability and entailment for the new logic are decidable in NEXPTIME and we give a matching lower bound for the original logic, which establishes NEXPTIME-completeness of the satisfiability and entailment problems for both of them. Our algorithm is based on a translation to 2-variable logic with counting quantifiers.