QuoteRef: holtAW11_1980

references g-h
discrete vs. continuous
event time
computer as state machine
state machine
Petri net
Petri net transitions and events
spatial vs. temporal representation


Holt, A.W., "A Mathematical Model of continuous discrete behavior", Wakefield, Massachusetts, Massachusetts Computer Associates, Inc., November 11, 1980. Google

1 ;;Quote: Zeno's paradoxes illustrates the problem of relating discrete to continuous
1 ;;Quote: objective experience is discrete but the world hangs together by the grace of continuity
1 ;;Quote: if this becomes that, it does so continuously; but without an hiatus, how is one to distinguish between this and that?
1 ;;Quote: when walking, one step leads continuously to the next yet steps are easily counted
2 ;;Quote: being in a state is being within a bounded region, while being in a transition is crossing a boundary
3 ;;Quote: being in a transition is interpretable as being within a bounded period of change
3 ;;Quote: states and transitions is like a hiker advancing from valley to valley by crossing a series of mountains
4 ;;Quote: a hiker going between valleys is like a clock whose ticks are the hiker's transitions from valley to ridge
7 ;;Quote: between states there are spatial boundaries and no temporal boundaries; the opposite holds for transitions
7 ;;Quote: a digital device is always in some state; so states partition its existential time and transitions are instantaneous
11 ;;Quote: associated with each atomic object is a set of possible states and a set of possible transitions
15 ;;Quote: the boundary of a region is all objects that are neither in the region nor out of the region
21 ;;Quote: a state space of regions and boundaries forms a topology of open and closed points; isomorphic with undirected Petri nets
29 ;;Quote: two regions of state space are 'separated' if their intersection is closed, 'joined' if the intersection is open, and 'inseparable' if same frame
33 ;;Quote: regions in transition space are processes with bounds called "begins" and "ends" instead of "entrance" and "exit"
40 ;;Quote: a object in transition is one state becoming another; neither pre-state nor post-state clearly holds
42 ;;Quote: atomic state can not have duration separate from the duration of the processes that hold the state
43 ;;Quote: an object can only be clearly in one state at a time or one transition at a time
43 ;;Quote: the states and transitions of an object cover its behavior with no gaps in space and time; creates a continuum out of discrete conditions
43 ;;Quote: a state and its bordering transitions are inseparable; can not resolve arguments about being clearly in a state or clearly in transition
43 ;;Quote: if a state clearly holds, then transitions for the state are unclear; and vice versa
46 ;;Quote: there is no boundary between 'clearly' and 'not clearly' yet 'clearly' has formal properties
47 ;;Quote: for atomic objects, a transition can have only one pre-state and post-state while states can have multiple pre/post-transitions

Related Topics up

ThesaHelp: references g-h (299 items)
Topic: discrete vs. continuous (47 items)
Topic: events (44 items)
Topic: state (35 items)
Topic: event time (44 items)
Topic: time (48 items)
Topic: computer as state machine (20 items)
Topic: state machine (67 items)
Topic: topology (29 items)
Topic: Petri net (44 items)
Group: formalism   (9 topics, 473 quotes)
Topic: Petri net transitions and events (21 items)
Topic: spatial vs. temporal representation (21 items)

Collected barberCB 1/83
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