Complexity Results for 1-safe Nets

Cheng, Allan; Esparza, Javier; Palsberg, Jens

doi:10.7146/dpb.v22i455.6773

Cited by 11 publications

(8 citation statements)

References 23 publications

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“…The decision of is NP-complete with respect to the size of the prefix of the unfolding, which computation is PSPACE [ 12 ]. Nevertheless, checking if , , and are satisfied can remain more tractable than checking the exact CTL property: uses the (complete) set of reachable states, but does not require the transitions.…”

Section: Resultsmentioning

confidence: 99%

“…We first show that bifurcation transitions can be completely identified using computation-tree temporal logic (CTL). However, this characterization relies extensively on the reachability problem, which is PSPACE-complete in ANs and similar frameworks [ 12 ], which limits its tractability. The main contribution of this paper is the introduction of an approximation of the bifurcation identification which is NP.…”

Section: Introductionmentioning

confidence: 99%

“…Given two states of an AN (or an equivalent Petri net), verifying is a PSPACE-complete problem [ 12 ].…”

Section: Introductionmentioning

confidence: 99%

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Identification of bifurcation transitions in biological regulatory networks using Answer-Set Programming

Fitime

Roux

Guziolowski

et al. 2017

Algorithms Mol Biol

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BackgroundNumerous cellular differentiation processes can be captured using discrete qualitative models of biological regulatory networks. These models describe the temporal evolution of the state of the network subject to different competing transitions, potentially leading the system to different attractors. This paper focusses on the formal identification of states and transitions that are crucial for preserving or pre-empting the reachability of a given behaviour.MethodsIn the context of non-deterministic automata networks, we propose a static identification of so-called bifurcations, i.e., transitions after which a given goal is no longer reachable. Such transitions are naturally good candidates for controlling the occurrence of the goal, notably by modulating their propensity. Our method combines Answer-Set Programming with static analysis of reachability properties to provide an under-approximation of all the existing bifurcations.ResultsWe illustrate our discrete bifurcation analysis on several models of biological systems, for which we identify transitions which impact the reachability of given long-term behaviour. In particular, we apply our implementation on a regulatory network among hundreds of biological species, supporting the scalability of our approach.ConclusionsOur method allows a formal and scalable identification of transitions which are responsible for the lost of capability to reach a given state. It can be applied to any asynchronous automata networks, which encompass Boolean and multi-valued models. An implementation is provided as part of the Pint software, available at http://loicpauleve.name/pint.Electronic supplementary materialThe online version of this article (doi:10.1186/s13015-017-0110-3) contains supplementary material, which is available to authorized users.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identification of bifurcation transitions in biological regulatory networks using Answer-Set Programming

Fitime

Roux

Guziolowski

et al. 2017

Algorithms Mol Biol

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“…We prove that the single-instance correctness and correctness problems for IO protocols are PSPACE-hard by reduction from the acceptance problem for bounded-tape Turing machines. We show that the standard simulation of boundedtape Turing machines by 1-safe Petri nets, as described for example in [20,29], can be modified to produce an IO protocol. This can be done for IO protocols but not for DO protocols: the simulation of the Turing machine relies on the fact that a transition will only occur in an IO protocol if an agent observes another agent in a certain state at the present moment.…”

Section: Correctness Of Io Protocols Is Pspace-hardmentioning

confidence: 99%

The complexity of verifying population protocols

et al. 2021

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Population protocols (Angluin et al. in PODC, 2004) are a model of distributed computation in which indistinguishable, finite-state agents interact in pairs to decide if their initial configuration, i.e., the initial number of agents in each state, satisfies a given property. In a seminal paper Angluin et al. classified population protocols according to their communication mechanism, and conducted an exhaustive study of the expressive power of each class, that is, of the properties they can decide (Angluin et al. in Distrib Comput 20(4):279–304, 2007). In this paper we study the correctness problem for population protocols, i.e., whether a given protocol decides a given property. A previous paper (Esparza et al. in Acta Inform 54(2):191–215, 2017) has shown that the problem is decidable for the main population protocol model, but at least as hard as the reachability problem for Petri nets, which has recently been proved to have non-elementary complexity. Motivated by this result, we study the computational complexity of the correctness problem for all other classes introduced by Angluin et al., some of which are less powerful than the main model. Our main results show that for the class of observation models the complexity of the problem is much lower, ranging from $$\varPi _2^p$$ Π 2 p to .

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“…The field of hardware verification seems to have been started in a little-known 1957 paper by Alonzo Church, 1903-1995, in which he described the use of logic to specify sequential circuits [11]. Today's semiconductor designs are still dominated by synchronous circuits.…”

Section: Introductionmentioning

confidence: 99%

Timed Petri Nets with Reset for Pipelined Synchronous Circuit Design

Parrot

Briday

Roux

2021

Application and Theory of Petri Nets and Concurrency

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This paper introduces an extension of Timed Petri Nets for the modeling of synchronous electronic circuits, addressing pipeline design problems. Petri Nets have been widely used for the modeling of electronic circuits. In particular, Timed Petri Nets which capture timing properties are perfectly suited for scheduling problems. Our extension, through reset that model the pipeline stages, and through delayable transitions that relax timing constraints, allows to widen the conception space of pipelined systems. After discussing maximal-step firing rule and the semantics of Timed Petri Nets "à la Ramchandani", we define our Timed Petri Nets with reset and delayable (non-asap) transitions. We then study the decidability and the complexity of the main problems of interest. We propose an abstraction of the state space. We then establish a translation of this model into a single-clock timed automata, which preserves the language. This translation settles the decidability on language inclusion and universality problems. Finally, an algorithm for the exploration of the state space is provided, and can be driven by the optimisation of various properties of the pipeline.

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Complexity Results for 1-safe Nets

Cited by 11 publications

References 23 publications

Identification of bifurcation transitions in biological regulatory networks using Answer-Set Programming

Identification of bifurcation transitions in biological regulatory networks using Answer-Set Programming

The complexity of verifying population protocols

Timed Petri Nets with Reset for Pipelined Synchronous Circuit Design

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