finite automata project

MODELING OF REACTIVE SYSTEMS WITH FINITE AUTOMATA

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MODELING OF REACTIVE SYSTEMS WITH FINITE FINITE AUTOMATA AUTOMATA Asma Hameed

Zarnigar Altaf

[email protected]

[email protected]

Syeda Phool Zehra [email protected]

Department of Computer Science, Fatima Jinnah Women University, The Mall, Rawalpindi, Pakistan.

Abstract: Finite automata are computing devices that accept/recognize regular languages and are used to model operations of many systems we find in practice. Finite-state machines can solve a large number of problems, among which are electronic design automation, communication protocol design, parsing and other engineering application. In biology and artificial intelligence research, state machine or hierarchies of state machines are some time used to describe neurological systems and in linguistics — to describe the grammars of natural languages .In this project we are describing modeling of reactive systems with Finite automata.

Keywords: Finite automata application ,modeling reactive system.

1. Introduction:

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eactive system that computes by reacting to stimuli from its environment along its Overall computation. 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, and lexical analyzers 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

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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.

2. Background Modeling is a visual process used for constructing and documenting the design and structure of an application. It is a good idea to make at least some outline of an application, showing interdependencies and relationships between the components and subsystems, during development. Here we are using finite automata for modeling of reactive system. Finite automata is used in software for verifying all kinds of systems with a finite number of states, such as communication protocols. Also used in software for scanning text, to find certain patterns. Used in “Lexical analyzers” of compilers (to turn program text into “tokens”, e.g. identifierz, keywords, brackets, punctuation).Part of Turing machines and abacus machines

3. Overview The term Finite automata' describes a class

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in the 1950's when they were viewed as abstract models of real circuits Finite automata (also called finite state machines, emerged during the 1940’s 1 940’s and 1950’s): useful e.g. text search, protocol verification, compilers, descriptions of certain formal grammars (N. Chomsky, 1950’s).Since 1950’s).Since then finite automata is being used in different machines.

4. Application Of Finite Automata Finite automata and various extensions of them, such as transducers, are used in areas as diverse as compilers, spelling checking, natural language grammar checking, communication protocol design, digital circuit simulation, digital flight control, speech recognition and synthesis, genetic sequencing, and Java program verification. Unfortunately, as the number of applications has grown, so has the variety of implementations and implementation techniques.

5. Advantages of FSM The advantages of finite automata is that their simplicity make it easy for inexperienced developers to implement with little to no extra knowledge (low entry level).Predictability (in deterministic FSM), given a set of inputs and a known current state, the state transition can be predicted, allowing for easy testing. Due to their simplicity, FSMs are quick to design, quick to implement and quick in execution.FSM is




of examples to learn from. FSMs are relatively flexible. There are a number of ways to implement a FSM based system in terms of topology, and it is easy to incorporate many other techniques .Easy to transfer from a meaningful abstract representation to a coded implementation .Easy determination of reach ability of a state, when represented in an abstract form, it is immediately obvious whether a state is achievable from another state, and what is required to achieve the state

5. Modeling Reactive With Finite Automata

Systems

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 those states can also be added to the model.

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5.1 Finite Automata Of Login Process For example consider the following very simplified version of login process to a computer from the computer point of view. Let us assume for simplicity that this computer accepts a single user at a time. Initially the computer waits for a user name to be typed in. This is one state of the system. When a name is typed in, it checks whether or not the name is valid. If it is valid, then it asks for and then waits for the password, which is another state. If the user name typed in is not valid, it goes back to the initial state. We could make it go to a different state and count the number of login attempts for security purpose. But let us make it simple. When a password is typed in and it is correct, then it accepts the user and starts a session. That is another state though it could further be broken down into a number of more states. When the session terminates, it gets a signal, goes back to the initial state and waits for another login. If the password typed in is incorrect, then it informs the user of that and waits for the next try. That is a fourth state. If the second password fails, it goes to the initial state and starts all over again. Again what we have seen is a model for one level of abstraction. Depending on how much detail we are interested in, different states would be identified and transitions would have to be selected accordingly.




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ACK. Again depending on the level of abstraction, different states and transitions would have to be chosen.

5.2 Finite Automata Of Communication Communication Protocol The next example is a protocol for a computer to follow in communicating with another computer. Again it is a very simplified version. Initially the computer is in wait state waiting for "Request for Next Message" (RFNM) to come from another computer. When a RFNM starts coming, it goes into the state of receiving it (Our interpretation is that the computer is in a state of receiving an RFNM and it is taking the action of receiving the RFNM) . Upon completion of the RFNM, it sends "Acknowledgement" (ACK) to the other computer, which is another state. After sending the ACK, it starts sending the requested message to the other party. When it is complete, it goes into another wait state waiting for an ACK to come from the other computer. If a negative ACK is received, it resends the message. If a positive ACK is received, it goes back to the initial state and waits for another RFNM to come. Thus a

5.3 Finite Automata Of Number Recognizer The third example is a system that recognizes numbers with or without a sign such as 5.378, -15, +213.8 etc. One such system initially waits for the first symbol to come in. If the first symbol is a sign, then it goes into a state, denote it by G, that indicates that a sign has been received. If the first digit is received before a decimal point, regardless of whether a sign has been read or not, it goes into a state, denote it by D, that indicates a digit has been read before a decimal point. If a decimal point is received before a digit, then it goes into a state, denote it by P, which indicates that a decimal point has been read. If a decimal point has been read (i.e. in state




reading a digit and stays there as long as digits are read. This Q is an accepting state. On the other hand if a digit has been read before a decimal point, i.e. it is in state D, then it can continue receiving digits and stay in D. D is another accepting state. If a decimal point is read while in D, then it goes to state P indicating that a decimal point has been read. This system can also be described by a regular expression. Since these numbers are represented by strings consisting of a possible sign, followed by zero or more digits, followed by a possible decimal point, followed by one or more digits, they can be represented by the following regular expression: +

+

+

+

(s+ + s- + ) ( d .d + d + .d ), where s+ and s- represent the positive and negative signs, respectively and d belongs to { 0 , 1 , 2 , . . . , 9 } . This system can be modeled by the following finite automaton:

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Conclusion After completing this project we have found that finite automata is a part of many machine and by modeling reactive system with finite automata we have got a diagrammatic representation of machines that how these machines work. Due to its advantages we use finite automata machine.

Acknowledgement First of all I thank ALLAH, the Almighty, for bestowing me with determination and grit to undergo the project. I owe my gratitude to many people for the guidance they endowed me with. Foremost on the list is Mr, Aihab Khan my supervisor, who was sheer source of guidance and encouragement. I am also gratified to my family whose suggestions have helped me to improve and render this project

References: [1] [1]http://aidepot.com/FiniteStateMachines/FSMBackground.html [2] [2]http://www.cs.umbc.edu/portal/help/theory/au tomata_def.shtml [3] [3]http://www.informit.com/articles/article.aspx ?p=27792 [4] [4]http://www.cs.odu.edu/~toida/nerzic/390tech ed/regular/fa/intr_2_fa.html




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finite automata project

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