Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Symbolic timing verification of timing diagrams using Presburger formulas
DAC '97 Proceedings of the 34th annual Design Automation Conference
Symbolic Model Checking
On the Construction of Automata from Linear Arithmetic Constraints
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
MONA 1.x: New Techniques for WS1S and WS2S
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
A Comparison of Presburger Engines for EFSM Reachability
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Diophantine Equations, Presburger Arithmetic and Finite Automata
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
RTL-Datapath Verification using Integer Linear Programming
ASP-DAC '02 Proceedings of the 2002 Asia and South Pacific Design Automation Conference
The convex hull of a regular set of integer vectors is polyhedral and effectively computable
Information Processing Letters
Bounded model checking of infinite state systems
Formal Methods in System Design
Bounds on the automata size for Presburger arithmetic
ACM Transactions on Computational Logic (TOCL)
A Geometric Constraint over k-Dimensional Objects and Shapes Subject to Business Rules
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Structural Presburger digit vector automata
Theoretical Computer Science
Cuts from Proofs: A Complete and Practical Technique for Solving Linear Inequalities over Integers
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
The convex hull of a regular set of integer vectors is polyhedral and effectively computable
Information Processing Letters
Verification of data paths using unbounded integers: automata strike back
HVC'06 Proceedings of the 2nd international Haifa verification conference on Hardware and software, verification and testing
A quantifier elimination algorithm for linear modular equations and disequations
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Cuts from proofs: a complete and practical technique for solving linear inequalities over integers
Formal Methods in System Design
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
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We present a new way of using Binary Decision Diagrams in automata based algorithms for solving the satisfiability problem of quantifier-free Presburger arithmetic. Unlike in previous approaches [5, 2, 19], we translate the satisfiability problem into a model checking problem and use the existing BDD-based model checker SMV [13] as our primary engine.We also compare the performance of various Presburger tools, based on both automata and ILP approaches, on a large suite of parameterized randomly generated test cases. The strengths and weaknesses of each approach as a function of these parameters are reported, and the reasons for the same are discussed. The results show that no single tool performs better than the others for all the parameters.On the theoretical side, we provide tighter bounds on the number of states of the automata.