Costs and rewards in priced timed automata

Conference item

We consider Pareto analysis of reachable states of multi-priced timed automata (MPTA): timed automata equipped with multiple observers that keep track of costs (to be minimised) and rewards (to be maximised) along a computation. Each observer has a constant non-negative derivative which may depend on the location of the MPTA. We study the Pareto Domination Problem, which asks whether it is possible to reach a target location via a run in which the accumulated costs and rewards Pareto dominate a given objective vector. We show that this problem is undecidable in general, but decidable for MPTA with at most three observers. For MPTA whose observers are all costs or all rewards, we show that the Pareto Domination Problem is PSPACE-complete. We also consider an ε-approximate Pareto Domination Problem that is decidable without restricting the number and types of observers. We develop connections between MPTA and Diophantine equations. Undecidability of the Pareto Domination Problem is shown by reduction from Hilbert's 10thProblem, while decidability for three observers is shown by a translation to a fragment of arithmetic involving quadratic forms.

Authors: Fränzle, M; Shirmohammadi, M; Swaminathan, M; Worrell, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Schloss Dagstuhl
• Journal: LIPIcs
• Volume: 107
• Pages: 125:1--125:14
• Series: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
• Publication date: 2018-06-29
• Acceptance date: 2018-04-15
• Event title: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
• Event location: Prague, Czech Republic
• Event start date: 2018-07-09
• Event end date: 2018-07-13
• DOI: 10.4230/LIPIcs.ICALP.2018.125
• ISSN: 1868-8969
• ISBN: 9783959770767
• Language: English
• Keywords: priced timed automata; pareto domination; diophantine equations