ISO/IEC 15909-1:2019 システムおよびソフトウェアエンジニアリング—高レベルのペトリネット—パート1：概念、定義、およびグラフィカル表記 | ページ 6

3.1

arc

directed edge of a net which may connect a place (3.28) to a transition (3.37) or a transition to a place, normally represented by an arrow

3.2

arc annotation

expression that may involve constants, variables and operators (3.21) used to annotate an arc (3.1) of a net

Note 1 to entry: The expression shall evaluate to a multiset (3.17) over the type of the arc’s associated place (3.28) .

3.3

basis set

set of objects used to create a multiset (3.17)

3.4

carrier

set of a many-sorted algebra (3.14)

3.5

concurrent enabling

<transition modes> state, for a multiset (3.17) of transition (3.37) modes, when all the involved input places (3.13) contain enough tokens to satisfy the sum of all of the demands imposed on them by each input arc (3.12) annotation (3.2) evaluated for each transition mode in the multiset

3.6

concurrency

property of a system in which events may occur independently of each other, and hence are not ordered

Note 1 to entry: See also step and concurrent enabling (3.5) .

3.7

declaration

set of statements which define the sets, constants, parameter (3.24) values, typed variables and functions required for defining the annotations on a high-level Petri net (3.9)

3.8

enabling

<a transition> state of a transition (3.37) in a particular mode and net marking (3.15) when the following conditions are met: the marking of each input place (3.13) of the transition satisfies the demand imposed on it by its arc annotation (3.2) evaluated for the particular transition mode; the demand is satisfied when the place’s marking contains (at least) the multiset (3.17) of tokens indicated by the evaluated arc annotation; the determination of transition modes guarantees that the Transition Condition is satisfied

Note 1 to entry: See concurrent enabling (3.5) .

3.9

high-level Petri net

high-level net

HLPN

algebraic structure comprising: a set of places (3.28) ; a set of transitions (3.37) ; a set of types; a function associating a type to each place, and a set of modes (a type) to each transition; a pre-function imposing token demands ( multisets (3.17) of tokens) on places for each transition mode; a post-function determining output tokens (multisets of tokens) for places for each transition mode; and an initial marking (3.10)

3.10

initial marking

<a net> set of initial making of places (3.11) given with the high-level net (3.9) definition

3.11

initial marking of place

special marking (3.15) of a place (3.28) , defined with the net

3.12

input arc

<a transition>arc directed from a place (3.28) to the transition (3.37)

3.13

input place

<a transition> place (3.28) connected to the transition (3.37) by an input arc (3.12)

3.14

many-sorted algebra

mathematical structure comprising a set of sets and a set of functions taking these sets as domains and co-domains

3.15

marking

<a net> set of the place (3.28) markings for all places of the net.

3.16

marking of a place

multiset (3.17) of tokens associated with (‘residing in’) the place (3.28)

3.17

multiset

bag

collection of items where repetition of items is allowed

3.18

multiplicity

natural number (i.e. non-negative integer) which describes the number of repetitions of an item in a multiset (3.17)

3.19

multiset cardinality

cardinality of a multiset

sum of the multiplicities of each of the members of the multiset (3.17)

3.20

node

vertex of a net graph, i.e. either a place (3.28) or a transition (3.37)

3.21

operator

symbol representing the name of a function

3.22

output arc

<a transition> arc directed from the transition (3.37) to a place (3.28)

3.23

output place

<a transition> place (3.28) connected to the transition (3.37) by an output arc (3.22)

3.24

parameter

symbol that can take a range of values defined by a set

Note 1 to entry: It is defined as a constant in the signature (3.32) .

3.25

Petri net

net

algebraic structure with two sets, one called places (3.28) and the other called transitions (3.37) , together with their associated relations and functions, and named after their inventor, Carl Adam Petri

3.26

Petri net with priorities

Petri net (3.25) having priorities which can be used for selecting the enabled transitions (3.37) according to the given priority scheme

Note 1 to entry: The firing rule is the same as a Petri net without priorities.

3.27

Petri net with time

Petri net (3.25) having timing constraints associated with the nodes (3.20) or arcs

Note 1 to entry: These constraints affect the enabling (3.8) and firing rules.

3.28

place

node (3.20) of a net, usually represented by an ellipse

3.29

place/transition net

P/T net

Petri net (3.25) comprising a net with positive integers associated with arcs and an initial marking (3.10) function which associates a natural number of simple tokens (‘black dots’) with places (3.28)

3.30

reachability graph

directed graph where the nodes (3.20) correspond to reachable markings (3.31) and the edges to transition (3.37) occurrences

3.31

reachable marking

marking (3.15) of the net that can be reached from the initial marking (3.10) by the occurrence of transitions (3.37)

3.32

signature

mathematical structure comprising a set of sorts (3.33) and a set of operators (3.21)

3.33

sort

symbol representing the name of a set

3.34

symmetric net

high-level Petri net (3.9) where types are finite and only built-in operations are allowed

3.35

term

expression comprising constants, variables and operators (3.21) built from a signature (3.32) and a set of sorted variables

3.36

time Petri net

Petri net (3.25) with time where timing constraints are associated with transitions (3.37)

3.37

transition

node (3.20) of a net, usually represented by a rectangle