The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Introduction to algorithms
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Postpass Code Optimization of Pipeline Constraints
ACM Transactions on Programming Languages and Systems (TOPLAS)
Automatic predicate abstraction of C programs
Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
Extended static checking for Java
PLDI '02 Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Negative-Cycle Detection Algorithms
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Proof Generation in the Touchstone Theorem Prover
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Zap: automated theorem proving for software analysis
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
From KSAT to Delayed Theory Combination: Exploiting DPLL Outside the SAT Domain
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Combining Decision Procedures by (Model-)Equality Propagation
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Annals of Mathematics and Artificial Intelligence
Theory decision by decomposition
Journal of Symbolic Computation
Exact join detection for convex polyhedra and other numerical abstractions
Computational Geometry: Theory and Applications
Weakly-relational shapes for numeric abstractions: improved algorithms and proofs of correctness
Formal Methods in System Design
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Incremental Satisfiability and Implication for UTVPI Constraints
INFORMS Journal on Computing
Symbolic modular deadlock analysis
Automated Software Engineering
Zap: automated theorem proving for software analysis
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Solving sparse linear constraints
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Combining decision procedures by (model-)equality propagation
Science of Computer Programming
Automated and efficient analysis of role-based access control with attributes
DBSec'12 Proceedings of the 26th Annual IFIP WG 11.3 conference on Data and Applications Security and Privacy
Minimum clique cover in claw-free perfect graphs and the weak Edmonds-Johnson property
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Lossless horizontal decomposition with domain constraints on interpreted attributes
BNCOD'13 Proceedings of the 29th British National conference on Big Data
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A unit two variable per inequality (UTVPI) constraint is of the form a.x+b.y ≤ d where x and y are integer variables, the coefficients a,b ∈ {–1,0,1} and the bound d is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given m such constraints over n variables, the procedure checks the satisfiability of the constraints in O(n.m) time and O(n+m) space. This improves upon the previously known O(n2.m) time and O(n2) space algorithm based on transitive closure. Our decision procedure is also equality generating, proof generating, and model generating.