1 ;;Quote: Petri assumed that metrics do not exist for space, time, or any physical magnitude

1 ;;Quote: time is a strictly, local relation between states

1 ;;Quote: in Petri net theory, discrete objects are combined and produced by finite techniques

2 ;;Quote: a computer can operate asynchronously, fully parallel, arbitrary extension without interruption

3 ;;Quote: automata theory and classical physics use a global, system state determined by the global, real time

4 ;;Quote: Petri net theory assumes upper bounds on signal speed and information density

4 ;;Quote: for an automaton to solve any recursive problem it must be extendable without bound

23 ;;Quote: users need a recursive definition of a problem but computers can't represent recursive definitions because of their finitude

29 ;;Quote: synchronous clocks require a closed chain of communication that includes both clocks

31 ;;Quote: use physically realistic properties for idealized logical elements; e.g., quantization, conservation, and reaction

32 ;;Quote: Petri net theory rejects all global properties

32 ;;Quote: a Petri net can be an infinite net because its parts can not communicate with arbitrarily far away parts

35 ;;Quote: an 'and' gate only works correctly if its inputs do not change; not physically realizable because of missing reaction

35 ;;Quote: a realizable 'and' gate has only one transition '1a 1b 0c -> 0a 0b 1c'; it produces a reaction

36 ;;Quote: a Petri net transition is an elementary process that can not be subdivided; occurs as one act

36 ;;Quote: a switching element only defines the temporal successor of a state

37 ;;Quote: by exchanging 0s and 1s a switching element becomes its dual; if the element also exchanges 0s for 1s, the dual equals reversing temporal direction

37 ;;Quote: the connexions of a switching element (a,b,c) are its domains of operation; at these places, it perceives 0- and 1-objects

40 ;;Quote: in Petri net theory define an object as a bit at a location; an object does not 'move'

43 ;;Quote: a conflict in a Petri net occurs when an object is on the left-hand side of multiple actions; indeterminate which actions actually occurs

43+;;Quote: a conflict in a Petri net occurs when an action can deactivate other actions

43 ;;Quote: a net is capable of communication if it has peripheral locations that belong to only one node

43+;;Quote: communicate between two Petri nets by identifying peripheral locations

45 ;;Quote: a Petri net can exactly describe a person's behavior; can communicate with other Petri nets; not conflict-free

52 ;;Quote: Petri constructed a Petri net representation of a Turing machine; used automatic tape constructors; equivalent to an infinite net

73 ;;Quote: can construct a Turing machine with a Petri net that satisfies the conditions of physical realizability; only need one kind of transition

75 ;;Quote: in a conflict-free net, the action is fully specified; otherwise have an incomplete net with information supplied from elsewhere

75 ;;Quote: the abstract description of a physical system is independent of temporal direction