The context-freeness of the languages associated with vector addition systems is decidable

Schwer, Sylviane

doi:10.1016/0304-3975(92)90002-w

Cited by 13 publications

(12 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This problem was shown to be decidable by Schwer in [9], but the proof is very complex and intricate. In this paper, we revisit the context-freeness problem for VAS.…”

Section: Vector Addition Systemsmentioning

confidence: 99%

“…In this paper, we focus on trace languages of VAS, that is, without action labeling nor acceptance condition. Schwer showed in [9] that context-freeness is decidable for trace languages of VAS. However, the proof is long (almost 50 pages), very complex and intricate, and the resulting decision procedure is based on five technical conditions on an unfolding of the coverability graph that ensures the "iterability" of loops (see also [10]).…”

Section: Introductionmentioning

confidence: 99%

“…Compared to [9], our approach does not use Ogden's Lemma, but is solely based on Ginsburg's characterization of bounded context-free languages [11]. This allows us to work with vectors of numbers instead of words.…”

Section: Introductionmentioning

confidence: 99%

“…The main source of inspiration for this work is Schwer's article [9], where it is shown that the contextfreeness problem for VAS is decidable. The complexity of this problem is still open.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Context-Freeness Problem for Vector Addition Systems

Leroux

Penelle

Sutre

2013

2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

Abstract-Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as boundedness, reachability, regularity, as well as contextfreeness, which is the focus of this paper. The context-freeness problem asks whether the trace language of a given VAS is context-free. This problem was shown to be decidable by Schwer in 1992, but the proof is very complex and intricate. The resulting decision procedure relies on five technical conditions over a customized coverability graph. These five conditions are shown to be necessary, but the proof that they are sufficient is only sketched. In this paper, we revisit the context-freeness problem for VAS, and give a simpler proof of decidability. Our approach is based on witnesses of non-context-freeness, that are bounded regular languages satisfying a nesting condition. As a corollary, we obtain that the trace language of a VAS is context-free if, and only if, it has a context-free intersection with every bounded regular language.

show abstract

“…This problem was shown to be decidable by Schwer in [9], but the proof is very complex and intricate. In this paper, we revisit the context-freeness problem for VAS.…”

Section: Vector Addition Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Context-Freeness Problem for Vector Addition Systems

Leroux

Penelle

Sutre

2013

2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

show abstract

“…This problem was shown to be decidable by Schwer in [14]. Since it is based on the coverability graph, the resulting algorithm's complexity is non-primitive recursive.…”

Section: Complexity Of the Context-freeness Problem For Vasmentioning

confidence: 99%

A Relational Trace Logic for Vector Addition Systems with Application to Context-Freeness

Leroux¹,

Praveen²,

Sutre³

2013

CONCUR 2013 – Concurrency Theory

View full text Add to dashboard Cite

Abstract. We introduce a logic for specifying trace properties of vector addition systems (VAS). This logic can express linear relations among pumping segments occurring in a trace. Given a VAS and a formula in the logic, we investigate the question whether the VAS contains a trace satisfying the formula. Our main contribution is an exponential space upper bound for this problem. The proof is based on a small model property for the logic. Compared to similar logics that are solvable in exponential space, a distinguishing feature of our logic is its ability to express non-context-freeness of the trace language of a VAS. This allows us to show that the context-freeness problem for VAS, whose complexity was not established so far, is ExpSpace-complete.

show abstract

Decidability and Complexity of Petri Net Problems

Haddad¹

2009

Petri Nets

View full text Add to dashboard Cite

The context-freeness of the languages associated with vector addition systems is decidable

Cited by 13 publications

References 17 publications

On the Context-Freeness Problem for Vector Addition Systems

On the Context-Freeness Problem for Vector Addition Systems

A Relational Trace Logic for Vector Addition Systems with Application to Context-Freeness

Decidability and Complexity of Petri Net Problems

Contact Info

Product

Resources

About