Application of Finite Automata -Djr

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We have seen an example of use of finite automata in describing the operation of a simplified version of vending machine. Many other systems operating in practice can also be modeled by finite automata such as control circuits of computers, computer network communication protocols, lexical analysers for compilers etc. Many of those systems fall into the class of systems called reactive system. A reactive system is a system that changes its actions, outputs and conditions/status in response to stimuli from within or outside it. It is an event driven or control driven system continuously having to react to external and/or internal stimuli. The inputs for a reactive system are never ready unlike for example when two numbers are added together by an adder (Here we are considering an adder at a higher level of abstraction than physical devices level ignoring for example the transient states of the electronic circuit that realizes an adder). An adder does not respond unless the input i.e. two numbers to be added are ready. A system such as an adder is called a transformational system. In the case of vending machine or communication protocol, on the other hand, a system must respond to each stimulus, even to a fragment of input such as each coin tossed in for a can of soda or every message received. 

It is generally agreed that finite automata are a natural medium to describe dynamic behaviors of reactive systems. Finite automata are formal and rigorous and computer programs can be easily written to simulate their behaviors.  To model a reactive system with finite automaton, first the states the system goes in or the modes of its operation are identified. These become the states of the finite automaton that models it. Then the transitions between the states triggered by events and conditions, external or internal to the system, are identified and they become arcs in the transition diagram of the finite automaton. In addition actions that may take place in...
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