Timed Automata and Logics for Real-time Systems

65 Pages·2014·0.62 MB·English

TimedTransitionSystems
TimedAutomata
NetworksofTimedAutomata
RegionsandRegionGraph
EquivalenceCheckingProblems
Timed Automata and Logics for Real-time Systems
Luca Aceto
ICE-TCS, School of Computer Science
Reykjavik University, Iceland
[email protected] and [email protected]
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co1m/43
TimedTransitionSystems
TimedAutomata
NetworksofTimedAutomata
RegionsandRegionGraph
EquivalenceCheckingProblems
Goals of the course
Learning outcomes
At the end of the course, you will
be familiar with the basic theory of timed automata,
be able to model and verify real-time systems using UPPAAL,
be familiar with
some of the behavioural equivalences over time automata and
some of the logics for real-time systems and their connections
with behavioural equivalences.
The course will be evaluated via a small-group project.
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co2m/43
TimedTransitionSystems
TimedAutomata
NetworksofTimedAutomata
RegionsandRegionGraph
EquivalenceCheckingProblems
Content of the first part of the course
labelled transition systems with time
timed automata
timed and untimed bisimilarity
timed and untimed language equivalence
region graph and the reachability problem
networks of timed automata
model checking of basic properties of timed automata
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co3m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
Need for Introducing Time-related Features
Timeouts in protocols:
In CCS, say, timeouts can be modelled using nondeterminism.
Enough to prove that the protocol is safe.
Maybe too abstract for certain questions. (What is the
average time to deliver the message?)
Many real-life systems depend on timing:
Real-time controllers (production lines, computers in cars,
railway crossings).
Embedded systems (mobile phones, remote controllers, digital
watch).
...
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co4m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
Labelled Transition Systems with Time
Timed (labelled) transition system (TLTS)
a
TLTS is a triple (Proc,Act,{−→| a ∈ Act}) where
Proc is a set of states (or processes),
Act = N ∪R≥0 is a set of actions (consisting of labels and
time-elapsing steps), and
a
for every a ∈ Act, −→ ⊆ Proc ×Proc is a binary relation on
states called the transition relation.
We write
s −→a s(cid:48) if a ∈ N and (s,s(cid:48)) ∈−→a , and
s −d→ s(cid:48) if d ∈ R≥0 and (s,s(cid:48)) ∈−d→.
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co5m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
Healthiness conditions on delay transitions
Typical requirements on the delay transitions
(Determinism) If s −d→ s(cid:48) and s −d→ s(cid:48)(cid:48) (d ∈ R≥0) then
s(cid:48) = s(cid:48)(cid:48).
(Zero delay) s −→0 s(cid:48) if, and only if, s = s(cid:48).
(Additivity 1) If s −d→ s(cid:48) −d→(cid:48) s(cid:48)(cid:48) then s d−+→d(cid:48) s(cid:48)(cid:48).
(Additivity 2) If s −d→ s(cid:48)(cid:48) and e ≤ d then s −e→ s(cid:48) −d−→e s(cid:48)(cid:48) for
some s(cid:48).
Why are these reasonable requirements?
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co6m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
How to Describe Timed Transition Systems?
Syntax Semantics
−→
unknown entity known entity
−→
CCS Labelled Transition Systems
−→
??? Timed Transition Systems
Timed Automata [Alur, Dill’90]
Finite-state automata equipped with clocks.
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co7m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
How to Describe Timed Transition Systems?
Syntax Semantics
−→
unknown entity known entity
−→
CCS Labelled Transition Systems
−→
??? Timed Transition Systems
Timed Automata [Alur, Dill’90]
Finite-state automata equipped with clocks.
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co7m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
How to Describe Timed Transition Systems?
Syntax Semantics
−→
unknown entity known entity
−→
CCS Labelled Transition Systems
−→
??? Timed Transition Systems
Timed Automata [Alur, Dill’90]
Finite-state automata equipped with clocks.
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co7m/43
TimedTransitionSystems
TimedAutomata Motivation
NetworksofTimedAutomata DefinitionofTLTS
RegionsandRegionGraph HowtoDescribeTimedTransitionSystems
EquivalenceCheckingProblems
How to Describe Timed Transition Systems?
Syntax Semantics
−→
unknown entity known entity
−→
CCS Labelled Transition Systems
−→
??? Timed Transition Systems
Timed Automata [Alur, Dill’90]
Finite-state automata equipped with clocks.
LucaAceto ICE-TCS,SchoolofComputerScience ReykjavikUnTiviemrseidty,[email protected]@sgtmeamisl.co7m/43