Finite petri nets as models for recursive causal behaviour

Ursula Goltz, Arend Rensink

    Research output: Contribution to journalArticleAcademicpeer-review

    4 Citations (Scopus)
    42 Downloads (Pure)

    Abstract

    Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: B=(a.nil | b.B)+c.nil. We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence.
    Original languageUndefined
    Pages (from-to)169-179
    Number of pages11
    JournalTheoretical computer science
    Volume124
    Issue number1
    DOIs
    Publication statusPublished - 1994

    Keywords

    • IR-18270
    • METIS-118790
    • EWI-8252

    Cite this

    @article{00e17354dc5546748d2f5ee3db278039,
    title = "Finite petri nets as models for recursive causal behaviour",
    abstract = "Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: B=(a.nil | b.B)+c.nil. We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence.",
    keywords = "IR-18270, METIS-118790, EWI-8252",
    author = "Ursula Goltz and Arend Rensink",
    year = "1994",
    doi = "10.1016/0304-3975(94)90058-2",
    language = "Undefined",
    volume = "124",
    pages = "169--179",
    journal = "Theoretical computer science",
    issn = "0304-3975",
    publisher = "Elsevier",
    number = "1",

    }

    Finite petri nets as models for recursive causal behaviour. / Goltz, Ursula; Rensink, Arend.

    In: Theoretical computer science, Vol. 124, No. 1, 1994, p. 169-179.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Finite petri nets as models for recursive causal behaviour

    AU - Goltz, Ursula

    AU - Rensink, Arend

    PY - 1994

    Y1 - 1994

    N2 - Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: B=(a.nil | b.B)+c.nil. We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence.

    AB - Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: B=(a.nil | b.B)+c.nil. We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence.

    KW - IR-18270

    KW - METIS-118790

    KW - EWI-8252

    U2 - 10.1016/0304-3975(94)90058-2

    DO - 10.1016/0304-3975(94)90058-2

    M3 - Article

    VL - 124

    SP - 169

    EP - 179

    JO - Theoretical computer science

    JF - Theoretical computer science

    SN - 0304-3975

    IS - 1

    ER -