Timed automata
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The document discusses timed automata, a formalism used to model real-time systems, consisting of finite automata with real-valued clocks and constraints. It provides formal definitions, representation methods, and tools for verification and analysis of timed automata, and highlights their applications in embedded systems and the need for real-time considerations in system design. The document also outlines the components of a network of timed automata combined into a single system using the calculus of communicating systems (CCS).
![Choice
The process P1 + P2 can proceed either as P1 or as P2.
Parallel composition
P1 | P2 says the both P1 and P2 can exist simuntaneously
Renaming
P1[b/a] means that all actions of a related to P1 are
renamed as b.
Restriction
P1a means that P1 is without the actions a.](https://image.slidesharecdn.com/timedautomata-170412063455/85/Timed-automata-9-320.jpg)
Timed automata
- 1. Timed Automata & Applications Submitted to : Mr. R.Siranjeevi Dept. Of CSE NIT Trichy Submitted by : Velamakanni Sri Sai Karthik CSE15U044
- 2. Outline : – Introduction – Formal definition – Representation of Timed Automata – Tools for Timed Automata – Network Timed Automata (CCS System) – Bottom Line – References
- 3. Introduction : ● Timed automata are a popular formalism to model real-time systems. They were introduced two decades ago to support formal verification. ● Timed Automata belongs to a special class of automata called Hybrid Automata. ● A timed automaton is essentially a finite automaton (that is a graph containing a finite extended with real-valued variables ) ,such an automaton may be considered as an abstract model of a timed system. ● A timed automaton is a finite state automaton with a set of asynchronous clocks(real valued) and a set of clock constraints.
- 4. Formal Definition : A timed automaton is a tuple A = (Q,Σ,C,E,q0) that consists of the following components: ● Q is a finite set. The elements of Q are called the states of A. ● Σ is a finite set called the alphabet or actions of A. ● C is a finite set called the clocks of A. ● E Q×Σ×B(C)×P(C)×Q is a set of edges, called transitions of A, where⊆ ● B(C) is the set of boolean clock constraints involving clocks from C, and ● P(C) is the powerset of C. ● q0 is an element of Q, called the initial state. ● An edge (q,a,g,r,q') from E is a transition from state q to q' with action a, guard g and clock resets r
- 5. Representaion of Timed Automata : ● An initial clock valuation maps each clock of a timed automaton to zero. ● A vertex in a timed automaton is called location. A location is associated with a clock constraint called the local invariant of that location. ● Control can stay in a location only if the clock valuation satisfies the local invariant of that location. ● An edge in a timed automaton is called a switch. A switch is associated with a clock constraint, a subset of the clocks, and a label (with a symbol). ● A clock constraint which is associated with a switch is called the guard of that switch.
- 6. ● The clock x is set to 0 each time the system switches from l0 to l1 on symbol a. The local invariant (x < 1) associated with the locations l1 and l2 ensures that the c-labeled switch from l2 to l3 happens within one time unit of the occurrence of a. ● Resetting clock y together with the b-labeled switch from l1 to l2 and the guard of the d-labeled switch from l3 to l0 ensures that the delay between b and the following d is always greater than two time units
- 7. Tools for Timed Automata : Name - latest release ● UPPAAL- 2011 ● IMITATOR-2011 ● RED - 2011 General Use ● Verification of real-time systems modeled as networks of timed automata(??). ● Extracting the largest safe subset of parameter values for a parametric timed automaton. ● A model checker and simulation checker for timed automata and parametric analyzer for parametric timed automata
- 8. Networks of Timed Automata : A network of timed automata is the parallel composition A 1|A 2|...|A n, of a set of timed automata A1 A2 ... An , called processes, combined into a single system by the CCS (Calculus of Communicating Systems) parallel composition operator with all external actions Hidden. CCS System: Given a set of action names, the set of CCS processes is defined by the following BNF(Backus Normal form) grammar: Syntax : The parts of the syntax are, in the order given above Empty process The empty process is a valid CCS process. Action the process a.P1 can perform an action a and continue as process P1. Process identifier Write to use identifier A for process P1
- 9. Choice The process P1 + P2 can proceed either as P1 or as P2. Parallel composition P1 | P2 says the both P1 and P2 can exist simuntaneously Renaming P1[b/a] means that all actions of a related to P1 are renamed as b. Restriction P1a means that P1 is without the actions a.
- 10. Bottom Line • Used in Embedded Systems, Mainframe computers etc.. • Although the decision to abstract away from quantitative time has had many advantages, it is ultimately Counterproductive when reasoning about systems that must interact with physical processes; the correct functioning of the control system of airplanes and toasters depends crucially upon real-time considerations. • The types of automata we have studied till now do not have any real-time considerations . • In only two decades the theory of timed automata has established itself as an integral part of real-time systems development . • Even Sequential logic can applied through Timed automata in UPPAAL. • By observing the origin dates of the variants and tools, it is clear that this area is becoming more active day by day.
- 11. References ● 1https://pdfs.semanticscholar.org/49eb/c99a52d66ad a968c937e0b417144d19fb0da.pdf ● https://en.wikipedia.org/wiki/Timed_automaton ● http://www.uppaal.org ● 2http://research.cs.queensu.ca/TechReports/Reports/ 2011-579.pdf ● Timed Automata for developement of Real-time Systems-Waez,Dingel,Rudie(Technical Report on Adavancements in recent Technologies)