The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
The shifting bottleneck procedure for job shop scheduling
Management Science
The MARUTI hard real-time operating system
ACM SIGOPS Operating Systems Review
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On Fourier's algorithm for linear arithmetic constraints
Journal of Automated Reasoning
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Software reliability via run-time result-checking
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Certifying algorithms for recognizing interval graphs and permutation graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum Propositional Proof Length is NP-Hard to Linearly Approximate
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Combining Logic and Optimization in Cutting Plane Theory
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Proceedings of the Second International Conference on Algebraic and Logic Programming
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Formal Verification of a Combination Decision Procedure
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Data-Structures for the Verification of Timed Automata
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
A hybrid SAT-based decision procedure for separation logic with uninterpreted functions
Proceedings of the 40th annual Design Automation Conference
Handbook of automated reasoning
Handbook of automated reasoning
Intriactability of Read-Once Resolution
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
An Analysis of Totally Clairvoyant Scheduling
Journal of Scheduling
Tutorial: Automated Formal Methods with PVS, SAL, and Yices
SEFM '06 Proceedings of the Fourth IEEE International Conference on Software Engineering and Formal Methods
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Hi-index | 0.00 |
This paper is concerned with determining the optimal length resolution refutation (OLRR) of a system of difference constraints over an integral domain. The problem of finding short explanations for unsatisfiable difference constraint systems (DCS) finds applications in a number of design domains including program verification, proof theory, real-time scheduling and operations research. It is well-known that resolution refutation is a sound and complete procedure to establish the unsatisfiability of boolean formulas in clausal form. The literature has also established that a variant of the resolution procedure called Fourier-Motzkin elimination is a sound and complete procedure for establishing the unsatisfiability of linear constraint systems (LCS). Our work in this paper first establishes that every DCS has a short (polynomial in the size of the input) resolution refutation and then shows that there exists a polynomial time algorithm to compute the optimal size refutation. One of the consequences of our work is that the Minimum Unsatisfiable Subset (MUS) of a DCS can be computed in polynomial time; computing the MUS of an unsatisfiable constraint set is an extremely important aspect of certifying algorithms.