What is the main difference between deterministic and nondeterministic finite state machines?
A deterministic finite state machine (DFSM) and a nondeterministic finite state machine (NFSM) are two types of finite state machines (FSMs) used in the field of computational complexity theory. While both FSMs have similar characteristics and can be used to model various computational processes, they differ in terms of their behavior and the nature of their transitions.
The main difference between a DFSM and an NFSM lies in the way they handle transitions between states. In a DFSM, the transition from one state to another is uniquely determined by the current state and the input symbol. This means that for a given state and input symbol, there can only be one possible next state. In other words, the DFSM operates in a deterministic manner, where the next state is uniquely determined by the current state and input.
On the other hand, an NFSM allows for multiple possible next states for a given state and input symbol. This means that the transition function of an NFSM can have multiple valid choices for the next state. In other words, the NFSM operates in a nondeterministic manner, where the next state is not uniquely determined by the current state and input. Instead, an NFSM can transition to one or more states simultaneously, creating multiple possible paths of computation.
To illustrate this difference, let's consider an example. Suppose we have an NFSM and a DFSM that both model a simple language that accepts strings of 0s and 1s ending with a 1. The NFSM has two states: S0 and S1. The DFSM also has two states: Q0 and Q1.
For the NFSM, the transition function for state S0 and input symbol 0 can have two possible next states: S0 and S1. This means that when the NFSM is in state S0 and receives the input symbol 0, it can transition to either state S0 or state S1. On the other hand, the transition function for state S0 and input symbol 1 has only one possible next state: S1. This means that when the NFSM is in state S0 and receives the input symbol 1, it will always transition to state S1.
In contrast, the DFSM has a unique next state for each combination of current state and input symbol. For example, when the DFSM is in state Q0 and receives the input symbol 0, it will always transition to state Q0. Similarly, when the DFSM is in state Q0 and receives the input symbol 1, it will always transition to state Q1.
The main difference between deterministic and nondeterministic finite state machines lies in the nature of their transitions. A deterministic finite state machine (DFSM) has a unique next state for each combination of current state and input symbol, while a nondeterministic finite state machine (NFSM) allows for multiple possible next states for a given combination of current state and input symbol.
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