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arXiv · 2307.07455

Real Equation Systems with Alternating Fixed-points (full version with proofs)

Jan Friso Groote·Tim A. C. Willemse
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Abstract

We introduce the notion of a Real Equation System (RES), which lifts Boolean Equation Systems (BESs) to the domain of extended real numbers. Our RESs allow arbitrary nesting of least and greatest fixed-point operators. We show that each RES can be rewritten into an equivalent RES in normal form. These normal forms provide the basis for a complete procedure to solve RESs. This employs the elimination of the fixed-point variable at the left side of an equation from its right-hand side, combined with a technique often referred to as Gau{\ss}-elimination. We illustrate how this framework can be used to verify quantitative modal formulas with alternating fixed-point operators interpreted over probabilistic labelled transition systems.

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Jan Friso Groote, Tim A. C. Willemse. 2023-07-14. Real Equation Systems with Alternating Fixed-points (full version with proofs). https://arxiv.org/abs/2307.07455

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