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If two finite state machines M and N are isomorphic, then
  • a)
    M can be transformed to N, merely re-labeling its states. .
  • b)
    M can he transformed to N, merely re-labeling its edges.
  • c)
    Me an be transformed to N, merely re-labeling its states and edges.
  • d)
    None of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If two finite state machines M and N are isomorphic, thena)M can be tr...
Understanding Isomorphic Finite State Machines
When we talk about two finite state machines (FSMs) M and N being isomorphic, we refer to a structural similarity between them. This means that they can be considered equivalent in terms of their state transition behavior, even if their states or transitions are labeled differently.
Key Points of Isomorphism
- State Re-labeling:
- Isomorphic FSMs can be transformed into one another by simply renaming their states.
- This indicates that each state in M corresponds to a unique state in N, preserving the transition structure.
- Edge Re-labeling:
- The edges (transitions) of an FSM are defined by their source and target states along with the input symbols that trigger them.
- While edges can be re-labeled, isomorphism primarily concerns the relationship between states rather than the labels on edges.
- Transformation Process:
- To transform M into N, a bijective mapping between the states of M and N is established, allowing for consistent transition behavior.
- The edges of M will follow the same transition rules after the states have been re-labeled, ensuring that the operational behavior remains unchanged.
Conclusion
Thus, the correct option is (a): M can be transformed to N, merely re-labeling its states. This encapsulates the essence of isomorphism in finite state machines, emphasizing that the structure of transitions remains intact while only state names vary. This concept is fundamental in understanding equivalence in computational systems.
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If two finite state machines M and N are isomorphic, thena)M can be transformed to N, merely re-labeling its states. .b)M can he transformed to N, merely re-labeling its edges.c)Me an be transformed to N, merely re-labeling its states and edges.d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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