Modelling time
in Real-time Systems
LAP 8780 and ISP 9010
Tallinn University of Technology
Professor Leo Motus
13.07.2017
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Why should we study time?
A man with a watch knows what time is;
a man with two watches isn’t so sure.
Anonymous
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Contents
1. Computer science has abstracted the time away
2. Real-time systems, and related software is based on
sciences of the artificial – i.e. synthesis based theory
3. The role of time in software
4. Examples of time usage
5. Philosophical and physical time
6. Metric time in OMG products
7. Timing analysis in RT UML and elsewhere
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E.A. Lee (1999) about conventional
computing science
Quantitative (metric) time has been systematically
removed from theories of computation.
Most of the temporal logics research deals with
“eventually” and “always”, where time is not a
quantifier but rather a qualifier.
Management of concurrency is trivial
Non-terminating programs fall into equivalence class of
defective programs – such programs form a major
class of programs in embedded systems
E.A.Lee “Embedded software –an agenda for research”, 1999
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Analysis based approach versus
synthesis based approach
H.A. Simon (1996) The Sciences of the Artificial, MIT Press
Science describes existing objects and their interactions,
while sciences of the artificial depart from a predefined
goal and synthesise objects with required properties.
Static environment assumption holds for Sciences (i.e.
natural sciences) and does not necessarily hold for
Sciences of the Artificial, because the synthesised
artefacts are usually at the interface of several
inhomogeneous domains
Sophisticated time is needed to match the properties of
different interacting domains – e.g. to complete
computation while static environment assumption holds.
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Evolution of the role of time in
software
Quantitative time has been gradually introduced to
computers and software in order to:
• Satisfy requirements on the overall duration of
computations – to measure performance (1965)
• Invoke programs so as to meet their deadlines and
improve performance of the system – scheduling
theory and temporal logics (since 1973)
• Directly monitor and influence the environment –
timing of interactions, validity of data, etc (since
1977)
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Examples of time usage
1.
2.
3.
4.
In natural science
In data and information processing
In simulation systems
In real-time systems
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What is time (pragmatically)?
Observation:
More complex systems (societies) rely more heavily on
the notion of time, as a basis for coordinated activities
The same applies to computer systems:
• transformation / number crunching oriented
systems – time as ordering of events is usually
sufficient
• embedded / real-time / proactive systems – more
sophisticated features of time are required
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What is time (philosophically)?
The essence of time is still an object of research – it is
increasingly believed to be a subjective category rather
than an objective category.
In computer systems the major role of time is to:
• approximate incompletely known causal relations
• enable the match between the behaviour of a
computer system and that of its environment
• compensate our insufficient capability to take the
known causal relations into account
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Time as used in natural sciences
Each mature science relies on a single concept of time:
• theoretical physics – time is just another coordinate
in a four dimensional space, i.e. time is fully
reversible
• thermodynamics and biology – time has strict
intrinsic direction and, as a rule, is not reversible
• psychology, and other sciences about conscious
awareness – time has strict intrinsic direction, it has
moving origin (the origin of time is always at the
present moment)
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Time as used in data and
information processing systems
Topological (non-metric) time – that can be reduced to
linear ordering of events, and distance between those
events is not of interest. Topological time is fully
reversible.
Topological time is represented by an instruction counter
in programs, or by the order of historical events
recorded by a history writer without applying
quantitative time labels.
Fully reversible metric time – in the cases if the
distance between events becomes important, e.g.
some temporal logics
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Time as used in simulation
systems
Major difference from data processing is the necessity
for multiple, fully reversible times
Separate time counting is required for each concurrently
running simulated entity. The use of metric time
prevails over the topological time.
Virtual time and time warp mechanism demonstrate
the most complex use of this concept – developed in
UCLA (approximately 1986)
Rumours – this system was used to guide and manage the 1st Gulf
war.
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Time as used in real-time,
embedded systems (1)
In addition to the time as used in data processing and
simulation systems, we need:
• strictly increasing time – not all the completed
actions can be redone
• time with the moving origin – for ensuring timeselective interactions
All these different time counts must be operational
simultaneously
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Time as used in real-time,
embedded systems (2)
• each process functions in increasing (thermodynamic)
time, which advances in grains
• inside each grain the time is fully reversible
• inside each grain a process may have many relative,
strictly increasing times (in addition to a fully reversible
time)
• for each pair of communicating processes there is a
separate relative time with moving origin (in addition to
all other times)
This example is taken from the Q-model
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Evolution of the role of observations
in physics and computer science
R. Milner, 1980, Calculus for Communicating Systems, LNCS no.92
The only way to observe a system is to interact with it. To
make two components to interact, means to let them
observe each other.
Peter Wegner (1998) “Towards empirical computer science”, 27 pp.
Newtonian, relativity, and quantum theories can be
distinguished by their models of the relation between
observers and observed systems
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More about observers in physics (1)
• Newtonian theory – observer is an external recorder
of behaviour (absolute space and time)
• Relativity theory – observer is part of the observed
system and distinguishes between properties that
• are invariant for all observers (e.g. causality)
• depend on an observer (e.g. mass, length,
simultaneity)
Properties of objects (mass, length) and relations among
events (simultaneity) have meaning only relative to an
observer (i.e. they loose absolute,Newtonian meaning)
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More about observers in physics (2)
• Quantum theory – takes the relativity of observers to
its logical conclusion, viewing independently existing
absolute relativity as unnecessary.
Quantum theorists have moved away from the view that
events are caused by an independently existing reality,
they believe that observed events do not require
causal explanation.
Observations involve an irreversible transfer of
knowledge from the observed system to the observer
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Different users of time in software
process (on the macroscopic scale)
Environment
including
Humans
*
*
Computer
system *
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Observer of the specification
stage (“specifier”)
Observer of the design and
verification stage (“verifier”)
Observer of the implementation
stage (“implementor”)
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Time bound terms used by
“implementor” (1)
• Physical time – counting cycles of a strictly periodical
physical process
• Logical time – counting significant events occurring
during program execution
• Absolute time – a reference is established in relation
to a global event (origin of time) for the system
• Relative time – a reference is established in relation
to a local event (origin of time) for the system
These primitives form the basis for defining more
sophisticated terms
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Time bound terms used by
“implementor” (2)
• Global time – a reference is valid for the whole
system (e.g. distributed systems)
• Local time – a reference is valid only for a part of the
system
• Synchronisation of computer times with Universal
Time Coordinate (UTC)
Conventionally,these terms have been oriented to a
single execution of a program (in concordance with the
algorithm theory)
None of these time count mechanisms accepts explicit
influence from outside of the computer system.
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Time bound terms used by a
“verifier” (1)
Verification has to demonstrate that all the behaviours
required by users, and fixed in the specification, and only
those, are generated by the implementation.
Verifiers often use logical time (qualitative order of events)
to reason about real-time properties in reactive systems.
The use of metric time (quantitative order of events) enable
to reason about time correctness in a larger class of
applications.
Verifiers work with models – since they must rely on formal
theories.
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Time bound terms used by a “verifier”
– a case of temporal logic (2)
http://plato.stanford.edu/entries/logic-temporal
• Temporal logic (usually a kind of modal logic) studies
how to represent temporal information in logical
framework (Arthur Prior, 1960)
• Philosophical discussions about time in temporal logic:
• If based on modal logic – past, present, and future
• If based on first order logic – earlier and later, but no
presence
• Founders – natural languages (A.Prior, 1967), AI
(J.F.Allen, 1984), computer science (A.Pnueli, 1977)
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Time bound terms used by a “verifier”
– a case of temporal logic (3)
Examples of temporal operators are:
before, after, during, since, until, always, …
F - it will some time be the case… ; G - it will always be the case …
Fp  Gp
Gp  Fp
• In metric time each temporal operator may have
several time-bound versions – typically upper-bound,
and lower-bound operators:
• upper-bound properties resemble liveness
properties
• lower-bound properties resemble safety properties
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Time bound terms as used by a
“specifier”
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About semantics of time
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Time bound terms used by a “verifier”
– a case of temporal logic (3)
• Linear metric time – used mainly or studying
universal properties of a program
• Branching metric time – usually concentrates on
existential properties of a program
B
A
C
D
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