@techreport{lahiri2005an,
author = {Lahiri, Shuvendu and Musuvathi, Madan},
title = {An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals},
year = {2005},
month = {May},
abstract = {Nelson and Oppen provided a methodology for modularly combining decision procedures for individual theories to construct a decision procedure for a combination of theories. In addition to providing a check for satisfiability, the individual decision procedures need to provide additional functionalities, including equality generation. In this paper, we propose a decision procedure for a conjunction of difference constraints over rationals (where the atomic formulas are of the form x łeq y + c or x < y + c). The procedure extends any negative cycle detection algorithm (like the Bellman-Ford algorithm) to generate (1) equalities between all pair of variables, (2) produce proofs and (3) generates models that can be extended by other theories in a Nelson-Oppen framework. All the operations mentioned above can be performed with only a linear overhead to the cycle detection algorithm, in the average case.},
url = {http://approjects.co.za/?big=en-us/research/publication/an-efficient-nelson-oppen-decision-procedure-for-difference-constraints-over-rationals/},
number = {MSR-TR-2005-61},
}