Integer and combinatorial optimization
Integer and combinatorial optimization
A practical algorithm for exact array dependence analysis
Communications of the ACM
Resolution for quantified Boolean formulas
Information and Computation
Symbolic timing verification of timing diagrams using Presburger formulas
DAC '97 Proceedings of the 34th annual Design Automation Conference
Journal of the ACM (JACM)
Properties of Programs and the First-Order Predicate Calculus
Journal of the ACM (JACM)
Composite model-checking: verification with type-specific symbolic representations
ACM Transactions on Software Engineering and Methodology (TOSEM)
Parametric Dispatching of Hard Real-Time Tasks
IEEE Transactions on Computers
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Tractable Fragments of Presburger Arithmetic
Theory of Computing Systems
An analysis of quantified linear programs
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
An empirical analysis of algorithms for partially Clairvoyant scheduling
International Journal of Parallel, Emergent and Distributed Systems
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In this paper, we present an out of order quantifier elimination algorithm for a class of Quantified Linear Programs (QLPs) called Standard Quantified Linear Programs (SQLPs). QLPs in general and SQLPs in particular are extremely useful constraint logic programming structures that find wide applicability in the modeling of real-time schedulability specifications; see Subramani [Subramani, K., 2005a. A comprehensive framework for specifying clairvoyance, constraints and periodicity in real-time scheduling. The Computer Journal 48 (3), 259-272]. Consequently any algorithmic advance in their solution has a strong practical impact. Prior to this work, the only known approaches to the solution of QLPs involved sequential variable elimination; see Subramani [Subramani, K., 2003b. An analysis of quantified linear programs. In: Calude, C.S. et al. (Eds.), Proceedings of the 4th International Conference on Discrete Mathematics and Theoretical Computer Science. DMTCS. In: Lecture Notes in Computer Science, vol. 2731. Springer-Verlag, pp. 265-277]. In the sequential approach, the innermost quantified variable is eliminated first, followed by the variable which then becomes the innermost quantified variable and so on, until we are left with a single variable from which the satisfiability of the original formula is easily deduced. This approach is applicable in both discrete and continuous domains; however, it is to be noted that the logic demanding the sequential approach requires that the variables are discrete-valued. To the best of our knowledge, the necessity for sequential elimination over continuous-valued variables has not been investigated in the literature. The techniques used in the development of our elimination algorithm may find applications in domains such as classical logic and finite model theory. The final aspect of our research concerns the structure-preserving nature of the algorithm that we introduce here; in general, it is not known whether discrete domains admit such elimination procedures.