Automatic discovery of API-level exploits
Proceedings of the 27th international conference on Software engineering
Generalizing symbolic execution to library classes
PASTE '05 Proceedings of the 6th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
Propositional Satisfiability and Constraint Programming: A comparative survey
ACM Computing Surveys (CSUR)
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Optimal Length Resolution Refutations of Difference Constraint Systems
Journal of Automated Reasoning
Interpolant Generation for UTVPI
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
SAT encodings of state-space reachability problems in numeric domains
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals
Electronic Notes in Theoretical Computer Science (ENTCS)
Zap: automated theorem proving for software analysis
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A SAT-based decision procedure for mixed logical/integer linear problems
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A scalable method for solving satisfiability of integer linear arithmetic logic
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Using statically computed invariants inside the predicate abstraction and refinement loop
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Solving sparse linear constraints
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Efficient satisfiability modulo theories via delayed theory combination
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Decision procedures customized for formal verification
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
On the satisfiability of modular arithmetic formulae
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Given a formula 驴 in quantifier-free Presburger arithmetic, it is well known that, if there is a satisfying solution to 驴, there is one whose size, measured in bits, is polynomially bounded in the size of 驴. In this paper, we consider a special class of quantifier-free Presburger formulas in which most linear constraints are separation (difference-bound) constraints, and the non-separation constraints are sparse. This class has been observed to commonly occur in software verification problems. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of non-separation constraints, in addition to traditional measures of formula size. In particular, the number of bits needed per integer variable is linear in the number of non-separation constraints and logarithmic in the number and size of non-zero coefficients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifier-free Presburger formula to an equi-satisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. We present empirical evidence indicating that this method can greatly outperform other decision procedures.