Reachability relations of timed pushdown automata

Clemente, Lorenzo; Lasota, Sławomir

doi:10.1016/j.jcss.2020.11.003

Cited by 3 publications

(6 citation statements)

References 20 publications

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“…However, an open question is whether this blowup can be avoided in practice. As noted earlier, there exist extensions [14,15] studied especially in the context of binary reachability, which are expressively strictly more powerful, for which decidability results are known. It would be interesting to see how we can extend the zone-based approach to those models.…”

Section: Discussion and Future Workmentioning

confidence: 99%

“…This results in a powerful model of pushdown timed automata (PDTA for short), in which the source of "infinity" is both from real-time and the unbounded stack. Unsurprisingly, this model and its variants have been widely studied over the last 20 years with several old and recent results on decidability of reachability, related problems and their complexity, including [1][2][3][4][5]10,[13][14][15][16]. A wide variety of techniques have been employed to solve these problems, from region-based abstractions, to using atoms and systems of constraints, to encoding into different logics etc.…”

Section: Introductionmentioning

confidence: 99%

“…Thus our approach can be applied to the other model as well by just untiming the stack. There are other more powerful extensions [14,15] studied especially in the context of binary reachability, where only theoretical results are known. We also remark that the idea of combining the subsumption relation between zones with an equivalence relation also occurs while tackling liveness, or Buchi acceptance, in timed automata.…”

Section: Introductionmentioning

confidence: 99%

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Fast Zone-Based Algorithms for Reachability in Pushdown Timed Automata

Akshay

Gastin

Prakash

2021

Computer Aided Verification

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Given the versatility of timed automata a huge body of work has evolved that considers extensions of timed automata. One extension that has received a lot of interest is timed automata with a, possibly unbounded, stack, also called pushdown timed automata (PDTA). While different algorithms have been given for reachability in different variants of this model, most of these results are purely theoretical and do not give rise to efficient implementations. One main reason for this is that none of these algorithms (and the implementations that exist) use the so-called zone-based abstraction, but rely either on the region-abstraction or other approaches, which are significantly harder to implement.In this paper, we show that a naive extension, using simulations, of the zone based reachability algorithm for the control state reachability problem of timed automata is not sound in the presence of a stack. To understand this better we give an inductive rule based view of the zone reachability algorithm for timed automata. This alternate view allows us to analyze and adapt the rules to also work for pushdown timed automata. We obtain the first zone-based algorithm for PDTA which is terminating, sound and complete. We implement our algorithm in the tool TChecker and perform experiments to show its efficacy, thus leading the way for more practical approaches to the verification of timed pushdown systems.

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Section: Discussion and Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fast Zone-Based Algorithms for Reachability in Pushdown Timed Automata

Akshay

Gastin

Prakash

2021

Computer Aided Verification

View full text Add to dashboard Cite

show abstract

“…This results in a powerful model of pushdown timed automata (PDTA for short), in which the source of "infinity" is both from real-time and the unbounded stack. Unsurprisingly, this model and its variants have been widely studied over the last 20 years with several old and recent results on decidability of reachability, related problems and their complexity, including [1,2,3,4,5,9,12,13,14,15,24]. And a wide variety of techniques have been employed to solve these problems, from region-based abstractions, to using atoms and systems of constraints, to encoding into different logics etc.…”

Section: Introductionmentioning

confidence: 99%

“…Thus our approach can be applied to the other model as well by just untiming the stack. There are other more powerful extensions [14,13] studied especially in the context of binary reachability, where only theoretical results are known. We also remark that the idea of combining the subsumption relation between zones with an equivalence relation also occurs while tackling liveness, or Buchi acceptance, in timed automata.…”

Section: Introductionmentioning

confidence: 99%

Fast zone-based algorithms for reachability in pushdown timed automata

Akshay,

Gastin,

Prakash

2021

Preprint

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Given the versatility of timed automata a huge body of work has evolved that considers extensions of timed automata. One extension that has received a lot of interest is timed automata with a, possibly unbounded, stack, thus obtaining the model of pushdown timed automata (PDTA). While different algorithms have been given for reachability in different variants of this model, most of these results are purely theoretical and do not give rise to efficient implementations. One main reason for this is that none of these algorithms (and the implementations that exist) use the so-called zone-based abstraction, but rely either on the region-abstraction or other approaches, which are significantly harder to implement. In this paper, we show that a naive extension using simulations of the zone based reachability algorithm for the control state reachability problem of timed automata is not sound in the presence of a stack. To understand this better we give an inductive rule based view of the zone reachability algorithm for timed automata. This alternate view allows us to analyze and adapt the rules to also work for pushdown timed automata. We obtain the first zone-based algorithm for PDTA which is terminating, sound and complete. We implement our algorithm in the tool TChecker and perform experiments to show its efficacy, thus leading the way for more practical approaches to the verification of timed pushdown systems.

show abstract

General-Nondeterministic Fuzzy Pushdown Automata and Their Languages

Zhou

Yang

2022

Communications in Computer and Information Science

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Reachability relations of timed pushdown automata

Cited by 3 publications

References 20 publications

Fast Zone-Based Algorithms for Reachability in Pushdown Timed Automata

Fast Zone-Based Algorithms for Reachability in Pushdown Timed Automata

Fast zone-based algorithms for reachability in pushdown timed automata

General-Nondeterministic Fuzzy Pushdown Automata and Their Languages

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