Petri nets and regular languages

Valk, Rüdiger; Vidal-Naquet, Guy

doi:10.1016/0022-0000(81)90067-2

Cited by 112 publications

(67 citation statements)

References 7 publications

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“…We will now give necessary and sufficient conditions for the set of firing sequences of an equational Petri net to be regular or context free, respectively. A characterization of those Petri nets generating a regular exhaustive language can be found in [9].…”

Section: Regular and Context Free Epnlsmentioning

confidence: 99%

Shuffle equations, parallel transition systems and equational Petri nets

Bloom

Sutner

1989

Tapsoft '89

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Section: Regular and Context Free Epnlsmentioning

confidence: 99%

Shuffle equations, parallel transition systems and equational Petri nets

Bloom

Sutner

1989

Tapsoft '89

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“…Since the task buffer is often implemented as a finite buffer, let us say of size d, if D > d holds then there is an execution of the system that leads to an overflow of the buffer, and to a possible crash. Our decision procedure for the boundedness problem uses the above reduction to Petri Nets, and the construction of a coverability graph [12,33,34].…”

Section: Introductionmentioning

confidence: 99%

“…Our correctness arguments through Petri Nets use powerful algorithmic tools developed for Petri Nets [12,33,34]. The reduction from the existence of a fair non-terminating run in a Petri Net to the existence of a certain finite run in its coverability graph uses techniques similar to [33].…”

Section: Introductionmentioning

confidence: 99%

Verifying liveness for asynchronous programs

GantyPierre¹,

MajumdarRupak²,

RybalchenkoAndrey³

2009

SIGPLAN Not.

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Asynchronous or "event-driven" programming is a popular technique to efficiently and flexibly manage concurrent interactions. In these programs, the programmer can post tasks that get stored in a task buffer and get executed atomically by a non-preemptive scheduler at a future point. We give a decision procedure for the fair termination property of asynchronous programs. The fair termination problem asks, given an asynchronous program and a fairness condition on its executions, does the program always terminate on fair executions? The fairness assumptions rule out certain undesired bad behaviors, such as where the scheduler ignores a set of posted tasks forever, or where a non-deterministic branch is always chosen in one direction. Since every liveness property reduces to a fair termination property, our decision procedure extends to liveness properties of asynchronous programs.Our decision procedure for the fair termination of asynchronous programs assumes all variables are finite-state. Even though variables are finite-state, asynchronous programs can have an unbounded stack from recursive calls made by tasks, as well as an unbounded task buffer of pending tasks. We show a reduction from the fair termination problem for asynchronous programs to fair termination problems on Petri Nets, and our main technical result is a reduction of the latter problem to Presburger satisfiability. Our decidability result is in contrast to multi-threaded recursive programs, for which liveness properties are undecidable.While we focus on fair termination, we show our reduction to Petri Nets can be used to prove related properties such as fair nonstarvation (every posted task is eventually executed) and safety properties such as boundedness (find a bound on the maximum number of posted tasks that can be in the task buffer at any point).

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“…This follows from [31,52]: (V, (q 0 , x 0 )) is simultaneously X-unbounded iff the coverability graph CG(V, (q 0 , x 0 )) (see e.g., [31,52]) contains an extended configuration (q, y) such that y(X) = ∞ (for α ∈ Z∪{∞}, we write α to denote any vector of dimension n ≥ 1 whose component values are α). More properties about coverability graphs are recalled below but just note that in the sequel, we show that the simultaneous unboundedness problem is ExpSpace-complete too.…”

Section: Runsmentioning

confidence: 99%

“…We also provide a witness pseudo-run characterization in which we sometimes admit negative component values. This turns out to be the right approach when a characterization from coverability graphs [31,52] already exists. Apart from this unorthodox adaptation of [45], in the counterpart of Rackoff's proof about the induction on the dimension, we provide an induction on the dimension and on the length of the properties to be verified (see Lemma 4.4).…”

Section: Introductionmentioning

confidence: 99%

On Selective Unboundedness of VASS

Demri

2010

Electron. Proc. Theor. Comput. Sci.

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Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, counter values, run lengths). Some of these features can be checked in exponential space by using Rackoff's proof or its variants, combined with Savitch's Theorem. However, the question is still open for many others, e.g., regularity detection problem and reversal-boundedness detection problem. In the paper, we introduce the class of generalized unboundedness properties that can be verified in exponential space by extending Rackoff's technique, sometimes in an unorthodox way. We obtain new optimal upper bounds, for example for place boundedness problem, reversal-boundedness detection (several variants are present in the paper), strong promptness detection problem and regularity detection. Our analysis is sufficiently refined so as to obtain a polynomial-space bound when the dimension is fixed.

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Petri nets and regular languages

Cited by 112 publications

References 7 publications

Shuffle equations, parallel transition systems and equational Petri nets

Shuffle equations, parallel transition systems and equational Petri nets

Verifying liveness for asynchronous programs

On Selective Unboundedness of VASS

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