The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
A technique for summarizing data access and its use in parallelism enhancing transformations
PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
Introduction to algorithms
Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Precise and efficient static array bound checking for large embedded C programs
Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation
Higher-Order and Symbolic Computation
Fast decision algorithms based on union and find
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Grids: a domain for analyzing the distribution of numerical values
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Widening operators for weakly-relational numeric abstractions
SAS'05 Proceedings of the 12th international conference on Static Analysis
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
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
Loop refinement using octagons and satisfiability
SSV'10 Proceedings of the 5th international conference on Systems software verification
Fast acceleration of ultimately periodic relations
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Deciding conditional termination
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
On the linear ranking problem for integer linear-constraint loops
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
Automated Reasoning and Mathematics
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Integer octagonal constraints (a.k.a. Unit Two Variables Per Inequality or UTVPI integer constraints) constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called tight closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n3) algorithm to compute the tight closure of a set of UTVPI integer constraints.