Staying Alive as Cheaply as Possible

Bouyer, Patricia; Brinksma, Ed; Larsen, Kim Guldstrand

doi:10.1007/978-3-540-24743-2_14

Cited by 49 publications

(88 citation statements)

References 21 publications

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“…The PSPACE upper bound can be proven using the cornerpoint abstraction R cp (A) of A (see [7]). The result then relies on the following lemma.…”

Section: The Universal L-problemsmentioning

confidence: 99%

“….n], which violates the lower-bound constraint: there is 0 ≤ i ≤ n such that c i < 0. Then applying [7,Prop. 3] we get that there is a finite path π in R cp (A) with the cost being smaller: this path violates the constraint as well.…”

Section: The Universal L-problemsmentioning

confidence: 99%

“…Then applying [7,Prop. 6], for every ε > 0, we get a real path whose cost is ε-close to that of π, hence becomes negative (for ε small enough).…”

Section: The Universal L-problemsmentioning

confidence: 99%

“…For proving the upper bound for the standard problems, we rely on the corner-point abstraction R cp (A) (see [7]). The case of ∃c.∀ ∞ L(c) is not very difficult.…”

Section: Lemma 12mentioning

confidence: 99%

“…We project on R cp (A), yielding an infinite weighted tree. For each index i there is a branch π i of length i of the tree, with overall weight better than that of [0..i] ( [7,Prop. 6]).…”

Section: Lemma 12mentioning

confidence: 99%

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Lower-bound-constrained runs in weighted timed automata

Bouyer

Larsen

Markey

2014

Performance Evaluation

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Abstract-We investigate a number of problems related to infinite runs of weighted timed automata, subject to lower-bound constraints on the accumulated weight. Closing an open problem from [10], we show that the existence of an infinite lower-boundconstrained run is-for us somewhat unexpectedly-undecidable for weighted timed automata with four or more clocks.This undecidability result assumes a fixed and known initial credit. We show that the related problem of existence of an initial credit for which there exists a feasible run is decidable in PSPACE. We also investigate the variant of these problems where only bounded-duration runs are considered, showing that this restriction makes our original problem decidable in NEXPTIME. Finally, we prove that the universal versions of all those problems (i.e, checking that all the considered runs satisfy the lower-bound constraint) are decidable in PSPACE.

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“…The PSPACE upper bound can be proven using the cornerpoint abstraction R cp (A) of A (see [7]). The result then relies on the following lemma.…”

Section: The Universal L-problemsmentioning

confidence: 99%

Section: The Universal L-problemsmentioning

confidence: 99%

“…Then applying [7,Prop. 6], for every ε > 0, we get a real path whose cost is ε-close to that of π, hence becomes negative (for ε small enough).…”

Section: The Universal L-problemsmentioning

confidence: 99%

“…For proving the upper bound for the standard problems, we rely on the corner-point abstraction R cp (A) (see [7]). The case of ∃c.∀ ∞ L(c) is not very difficult.…”

Section: Lemma 12mentioning

confidence: 99%

“…We project on R cp (A), yielding an infinite weighted tree. For each index i there is a branch π i of length i of the tree, with overall weight better than that of [0..i] ( [7,Prop. 6]).…”

Section: Lemma 12mentioning

confidence: 99%

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