Revisiting Underapproximate Reachability for Multipushdown Systems

Akshay, S.; Gastin, Paul; Krishna, Shankara Narayanan; Roychowdhury, Sparsa

doi:10.1007/978-3-030-45190-5_21

Cited by 4 publications

(8 citation statements)

References 27 publications

(61 reference statements)

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“…Furthermore, after their introduction [25] scope-bounded multi-pushdown systems have been studied in terms of accepted languages [26], temporal logic model checking [28,3]. Moreover, scope-boundedness has been studied in the timed setting [2], [4].…”

Section: Related Workmentioning

confidence: 99%

Scope-Bounded Reachability in Valence Systems

Shetty,

Krishna,

Zetzsche

2021

Preprint

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Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in this underapproximation becomes decidable. One such underapproximation that covers a relatively high portion of runs is scope boundedness. In such a run, after each push to stack i, the corresponding pop operation must come within a bounded number of visits to stack i.In this work, we generalize this approach to a large class of infinite-state systems. For this, we consider the model of valence systems, which consist of a finite-state control and an infinitestate storage mechanism that is specified by a finite undirected graph. This framework captures pushdowns, vector addition systems, integer vector addition systems, and combinations thereof. For this framework, we propose a notion of scope boundedness that coincides with the classical notion when the storage mechanism happens to be a multi-pushdown.We show that with this notion, reachability can be decided in PSPACE for every storage mechanism in the framework. Moreover, we describe the full complexity landscape of this problem across all storage mechanisms, both in the case of (i) the scope bound being given as input and (ii) for fixed scope bounds. Finally, we provide an almost complete description of the complexity landscape if even a description of the storage mechanism is part of the input.

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Section: Related Workmentioning

confidence: 99%

Scope-Bounded Reachability in Valence Systems

Shetty,

Krishna,

Zetzsche

2021

Preprint

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“…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%

“…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. However, except for [4,5], to the best of our knowledge, none of the others carry an implementation. In [5], the implementation uses a tree-automaton implicitly based on regions and the focus in [4] is towards multi-pushdown systems.…”

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.

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%

Fast zone-based algorithms for reachability in pushdown timed automata

Akshay,

Gastin,

Prakash

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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

Revisiting Underapproximate Reachability for Multipushdown Systems

Cited by 4 publications

References 27 publications

Scope-Bounded Reachability in Valence Systems

Scope-Bounded Reachability in Valence Systems

Fast Zone-Based Algorithms for Reachability in Pushdown Timed Automata

Fast zone-based algorithms for reachability in pushdown timed automata

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