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## QuoteRef: holtAW11_1980

ThesaHelp:
references g-h
Topic:
discrete vs. continuous
Topic:
events
Topic:
state
Topic:
event time
Topic:
time
Topic:
computer as state machine
Topic:
state machine
Topic:
topology
Topic:
Petri net
Group:
formalism
Topic:
Petri net transitions and events
Topic:
spatial vs. temporal representation

#### Reference

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

Quotations
 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

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)

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