Towards mechanical metamathematics
Journal of Automated Reasoning
Artificial Intelligence - Special issue on knowledge representation
Formal Verification for Fault-Tolerant Architectures: Prolegomena to the Design of PVS
IEEE Transactions on Software Engineering
Principles and Pragmatics of Subtyping in PVS
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Formal Verification of a Combination Decision Procedure
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A Certified Version of Buchberger's Algorithm
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
"Ratio Regions": A Technique for Image Segmentation
ICPR '96 Proceedings of the 13th International Conference on Pattern Recognition - Volume 2
A Zero-Space algorithm for Negative Cost Cycle Detection in networks
Journal of Discrete Algorithms
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Stressing is better than relaxing for negative cost cycle detection in networks
ADHOC-NOW'05 Proceedings of the 4th international conference on Ad-Hoc, Mobile, and Wireless Networks
Fast and flexible difference constraint propagation for DPLL(T)
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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The negative cost cycle detection (NCCD) problem in weighted directed graphs is a fundamental problems in theoretical computer science with applications in a wide range of domains ranging from maximum flows to image segmentation. From the perspective of program verification, this problem is identical to the problem of checking the satisfiability of a conjunction of difference constraints. There exist a number of approaches in the literature for NCCD with each approach having its own set of advantages. Recently, a greedy, space-efficient algorithm called the stressing algorithm was proposed for this problem. In this paper, we present a novel proof of the Stressing algorithm and its verification using the Prototype Verification System (PVS) theorem prover. This example is part of a larger research program to verify the soundness and completeness of a core set of decision procedures.