Automated deduction by theory resolution
Journal of Automated Reasoning
Presburger arithmetic with unary predicates is P11 complete
Journal of Symbolic Logic
Extended static checking for Java
PLDI '02 Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation
Set Constraints: Results, Applications, and Future Directions
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Parameterized Verification with Automatically Computed Inductive Assertions
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
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
Satisfiability solving for software verification
International Journal on Software Tools for Technology Transfer (STTT)
Decidability of invariant validation for paramaterized systems
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Decidable fragments of many-sorted logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
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
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
What else is decidable about integer arrays?
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Boogie: a modular reusable verifier for object-oriented programs
FMCO'05 Proceedings of the 4th international conference on Formal Methods for Components and Objects
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Tapas: Theory Combinations and Practical Applications
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Symbolic heap abstraction with demand-driven axiomatization of memory invariants
Proceedings of the ACM international conference on Object oriented programming systems languages and applications
Instantiation of SMT problems modulo integers
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Test data generation for programs with quantified first-order logic specifications
ICTSS'10 Proceedings of the 22nd IFIP WG 6.1 international conference on Testing software and systems
Towards complete reasoning about axiomatic specifications
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Automatically inferring quantified loop invariants by algorithmic learning from simple templates
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Satisfiability solving and model generation for quantified first-order logic formulas
FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
Service Oriented Computing and Applications
Encoding industrial hardware verification problems into effectively propositional logic
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Efficiently solving quantified bit-vector formulas
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Relational reasoning via SMT solving
FM'11 Proceedings of the 17th international conference on Formal methods
Information Processing Letters
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Verifying low-level implementations of high-level datatypes
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
Bugs, moles and skeletons: symbolic reasoning for software development
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
E-Matching with free variables
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
ABZ'12 Proceedings of the Third international conference on Abstract State Machines, Alloy, B, VDM, and Z
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
A small model theorem for rectangular hybrid automata networks
FMOODS'12/FORTE'12 Proceedings of the 14th joint IFIP WG 6.1 international conference and Proceedings of the 32nd IFIP WG 6.1 international conference on Formal Techniques for Distributed Systems
Theories, solvers and static analysis by abstract interpretation
Journal of the ACM (JACM)
On verifying ATL transformations using 'off-the-shelf' SMT solvers
MODELS'12 Proceedings of the 15th international conference on Model Driven Engineering Languages and Systems
Accurate invariant checking for programs manipulating lists and arrays with infinite data
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Complete instantiation-based interpolation
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Efficiently solving quantified bit-vector formulas
Formal Methods in System Design
Instantiation Schemes for Nested Theories
ACM Transactions on Computational Logic (TOCL)
Hierarchic superposition with weak abstraction
CADE'13 Proceedings of the 24th international conference on Automated Deduction
Quantifier instantiation techniques for finite model finding in SMT
CADE'13 Proceedings of the 24th international conference on Automated Deduction
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Array Theory of Bounded Elements and its Applications
Journal of Automated Reasoning
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Quantifier reasoning in Satisfiability Modulo Theories (SMT) is a long-standing challenge. The practical method employed in modern SMT solvers is to instantiate quantified formulas based on heuristics, which is not refutationally complete even for pure first-order logic. We present several decidable fragments of first order logic modulo theories. We show how to construct models for satisfiable formulas in these fragments. For richer undecidable fragments, we discuss conditions under which our procedure is refutationally complete. We also describe useful heuristics based on model checking for prioritizing or avoiding instantiations.