State Transition Table - Example

Example

An example of a state transition table for a machine M together with the corresponding state diagram is given below.

State Transition Table
Input
State		 1 0
S1 S1 S2
S2 S2 S1
State Diagram

All the possible inputs to the machine are enumerated across the columns of the table. All the possible states are enumerated across the rows. From the state transition table given above, it is easy to see that if the machine is in S1 (the first row), and the next input is character 1, the machine will stay in S1. If a character 0 arrives, the machine will transition to S2 as can be seen from the second column. In the diagram this is denoted by the arrow from S1 to S2 labeled with a 0.

For a nondeterministic finite automaton (NFA), a new input may cause the machine to be in more than one state, hence its non-determinism. This is denoted in a state transition table by a pair of curly braces { } with the set of all target states between them. An example is given below.

State Transition Table for an NFA
Input
State		 1 0 ε
S1 S1 { S2, S3 } Φ
S2 S2 S1 Φ
S3 S2 S1 S1

Here, a nondeterministic machine in the state S1 reading an input of 0 will cause it to be in two states at the same time, the states S2 and S3. The last column defines the legal transition of states of the special character, ε. This special character allows the NFA to move to a different state when given no input. In state S3, the NFA may move to S1 without consuming an input character. The two cases above make the finite automaton described non-deterministic.

Read more about this topic:  State Transition Table

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