finite automata
Lesson 3 Finite Automata with Output
Three types of automata are studied in Formal Language Theory. *
Acceptor
The symbols of the sequence
s(1) s(2) … s(i) … s(t)
are presented sequentially to a machine M. M responds with a binary signal to each input. If the string scanned so far is accepted, then the light goes on, else the light is off.
A language acceptor
* Lesson 3 employs the treatment of this subject as found in Machines, Languages, and Computation by Denning, Dennis and Qualitz , Prentice-Hall.
Transducer
Abstract machines that operate as transducers are of interest in connection with the translation of languages. The following transducer produces a sentence
r(1) r(2) … r(n)
in response to the input sentence
s(1) s(2) … s(m)
If this machine is deterministic, then each sentence of an input language is translated into a specific sentence of an output language.
Generator
When M is started from its initial state, it emits a sequence of symbols
r(1) r(2) … r(i) … r(t)
from a set known as its output alphabet.
We will begin our study with the transducer model of abstract machine (or automaton). We often refer to such a device as a Finite State Machine (FSM) or as an automaton with output.
Finite State Machine (FSM)
The FSM model arises naturally from physical settings in which information-denoting signals are processed. Physical reality dictates that such systems are finite.
Only a finite number of operations may be performed in a finite amount of time. Such systems are necessarily discrete.
Problems are quite naturally decomposed into sequences of steps – hence our model is sequential.
We require that our machine not be subject to uncertainty, hence its behavior is deterministic.
There are two finite state machine models :
Mealy model – in which outputs occur during transitions.
Three types of automata are studied in Formal Language Theory. *
Acceptor
The symbols of the sequence
s(1) s(2) … s(i) … s(t)
are presented sequentially to a machine M. M responds with a binary signal to each input. If the string scanned so far is accepted, then the light goes on, else the light is off.
A language acceptor
* Lesson 3 employs the treatment of this subject as found in Machines, Languages, and Computation by Denning, Dennis and Qualitz , Prentice-Hall.
Transducer
Abstract machines that operate as transducers are of interest in connection with the translation of languages. The following transducer produces a sentence
r(1) r(2) … r(n)
in response to the input sentence
s(1) s(2) … s(m)
If this machine is deterministic, then each sentence of an input language is translated into a specific sentence of an output language.
Generator
When M is started from its initial state, it emits a sequence of symbols
r(1) r(2) … r(i) … r(t)
from a set known as its output alphabet.
We will begin our study with the transducer model of abstract machine (or automaton). We often refer to such a device as a Finite State Machine (FSM) or as an automaton with output.
Finite State Machine (FSM)
The FSM model arises naturally from physical settings in which information-denoting signals are processed. Physical reality dictates that such systems are finite.
Only a finite number of operations may be performed in a finite amount of time. Such systems are necessarily discrete.
Problems are quite naturally decomposed into sequences of steps – hence our model is sequential.
We require that our machine not be subject to uncertainty, hence its behavior is deterministic.
There are two finite state machine models :
Mealy model – in which outputs occur during transitions.