Parametric updates in parametric timed automata

André, Étienne; Lime, Didier; Ramparison, Mathias

doi:10.23638/lmcs-17(2:13)2021

Cited by 5 publications

(5 citation statements)

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“…Recall that the synthesis is intractable for bounded IP-PTAs (from Corollary 4.8) and for bounded L/U-PTAs. In contrast, and although studying reset-PTAs in detail goes beyond the scope of this work, we showed in [ALR21] that exact synthesis can be computed for bounded reset-PTAs as defined here, even when resets are done to (rational-valued) parameters.…”

Section: 1mentioning

confidence: 92%

“…L-PTAs with integer-valued parameters)-and therefore not part of Table 5. Clearly, beyond the obvious case of bounded PTAs with integer-valued parameters [JLR15], only two subclasses allow for exact synthesis: integer-valued L-PTAs [BLT09] and bounded-reset PTAs [ALR21]. The case of L-PTAs or U-PTAs over non-necessarily integer parameters remains open.…”

Section: Liveness Propertiesmentioning

confidence: 99%

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Reachability and liveness in parametric timed automata

André¹,

Lime²,

Roux³

2022

Logical Methods in Computer Science

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We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric reachability emptiness problem, i.e., the emptiness of the parameter valuations set allowing to reach some given discrete state, is undecidable. Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve decidability for reachability properties by enforcing a separation of parameters used as upper bounds in the automaton constraints, and those used as lower bounds. In this paper, we first study reachability. We exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Using this class, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses such as L/U-PTAs. We then study liveness. We prove that: (1) deciding the existence of at least one parameter valuation for which there exists an infinite run in an L/U-PTA is PSpace-complete; (2) the existence of a parameter valuation such that the system has a deadlock is however undecidable; (3) the problem of the existence of a valuation for which a run remains in a given set of locations exhibits a very thin border between decidability and undecidability.

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Section: 1mentioning

confidence: 92%

Section: Liveness Propertiesmentioning

confidence: 99%

Reachability and liveness in parametric timed automata

André¹,

Lime²,

Roux³

2022

Logical Methods in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…The only known situations when exact reachability-synthesis (i.e., synthesis of all parameter valuations for which a given location is reachable) can be achieved for subclasses of PTAs are 1. reachability-synthesis for U-PTAs (resp. L-PTAs) over integer-valued timing parameters [BL09]; 2. reachability-synthesis for the whole PTA class, over bounded and integervalued parameters (which reduces to TAs) [JLR15]; and 3. reachability-synthesis for reset-update-to-parameters-PTAs ("R-U2P-PTAs"), in which all clocks must be updated (possibly to a parameter) whenever a clock is compared to a parameter in a guard [ALR21].…”

Section: Related Workmentioning

confidence: 99%

Zone extrapolations in parametric timed automata

Arcile,

André

2022

Preprint

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Timed automata (TAs) are an efficient formalism to model and verify systems with hard timing constraints, and concurrency. While TAs assume exact timing constants with infinite precision, parametric TAs (PTAs) leverage this limitation and increase their expressiveness, at the cost of undecidability. A practical explanation for the efficiency of TAs is zone extrapolation, where clock valuations beyond a given constant are considered equivalent. This concept cannot be easily extended to PTAs, due to the fact that parameters can be unbounded. In this work, we propose several definitions of extrapolation for PTAs based on the M -extrapolation, and we study their correctness. Our experiments show an overall decrease of the computation time and, most importantly, allow termination of some previously unsolvable benchmarks.

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“…The only known situations when exact reachability-synthesis (i.e., synthesis of all parameter valuations for which a given location is reachable) can be achieved for subclasses of PTAs are 1. reachability-synthesis for PTAs with a single clock [2,10]; 2. reachability-synthesis for U-PTAs (resp. L-PTAs) over integer-valued timing parameters [19]; 3. reachability-synthesis for the whole PTA class, over bounded and integer-valued parameters (which reduces to TAs) [25]; and 4. reachability-synthesis for reset-update-toparameters-PTAs ("R-U2P-PTAs"), in which all clocks must be updated (possibly to a parameter) whenever a clock is compared to a parameter in a guard [11]. On the negative side, even L/U-PTAs show negative results for synthesis: while reachabilityemptiness is decidable for L/U-PTAs [24], reachability-synthesis is intractable (its result cannot be represented in general using a finite union of polyhedra) [25]; and even in the very restricted subclass of U-PTAs without invariant, TCTLemptiness (i.e., the emptiness of the parameter valuations set for which a TCTL formula is valid) is undecidable [9].…”

Section: Parameter Synthesis For Ptasmentioning

confidence: 99%

“…Precisely, given a reference valuation v, the expected result should be the open interval [⌊v(p)⌋, ⌊v(p)⌋ + 1) (where ⌊v(p)⌋ denotes the integral part of v(p)). For example, given v(p) = 10.3, the expected result is [10,11).…”

Section: Trace Preservationmentioning

confidence: 99%

Zone extrapolations in parametric timed automata

Arcile

André

2022

Preprint

View full text Add to dashboard Cite

Timed automata (TAs) are an efficient formalism to model and verify systems with hard timing constraints, and concurrency.While TAs assume exact timing constants with infinite precision, parametric timed automata (PTAs) leverage this limitation and increase their expressiveness, at the cost of undecidability.A practical explanation for the efficiency of TAs is zone extrapolation, where clock valuations beyond a given constant are considered equivalent.This concept cannot be easily extended to PTAs, due to the fact that parameters can be unbounded, meaning that the constants compared to the clocks have no upper bound.In this work, we propose several definitions of extrapolation for PTAs, and we study their correctness.Our experiments show an overall decrease of the computation time and, most importantly, allow termination of some previously unsolvable benchmarks.

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Parametric updates in parametric timed automata

Cited by 5 publications

References 0 publications

Reachability and liveness in parametric timed automata

Reachability and liveness in parametric timed automata

Zone extrapolations in parametric timed automata

Zone extrapolations in parametric timed automata

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