Transition System & Transition Table

Transition System(Or Graph) :

 A transition system or transition graph is a finite directed labelled graph in which each vertex represents a state and the directed edges indicate of a state and the edges are labelled with input/output.

These diagrams shows a transition system and initial and final states.

Numerical : Consider the transition system given in figure below

Determine the initial states, final states and the acceptability of 101011,111010.

Solution:   initial states are q0 and q1.

               Final states are q3.

For string 101011, the path value is q0 q0 q2 q3. since q3 is the final state so this string is accepted by above transition system.

for string 111010, there is no path value. so this string is not accepted by above transition system.

[ Trick : for checking the string acceptability, we start the string from initial state. if we reach the final state after completing the string, then we say that this string is accepted by transition system or not.]

Transition Table :

The above diagram shows that the transition table and the transition graph corresponding to the transition table.

Transition table is nothing but the tabular representation of the tarnsition graph or transition system.