The automaton which allows transformation to a new state without consuming any input symbols:

The automaton that allows transformation to a new state without consuming any input symbols is known as a Non-deterministic Finite Automaton with ε-transitions (NFA-ε). Here are the steps to understand this:

1. An automaton is a mathematical model for a machine with a finite number of states. It is used in computer science to understand how computations or processes behave.

2. There are different types of automata, including Deterministic Finite Automata (DFA), Non-deterministic Finite Automata (NFA), and Non-deterministic Finite Automata with ε-transitions (NFA-ε).

3. In a DFA, for each state and each input symbol, there is exactly one transition to a new state. This means that the machine must consume an input symbol to move to a new state.

4. In an NFA, for each state and each input symbol, there can be several possible next states. This means that the machine can move to different states for the same input symbol.

5. In an NFA-ε, the machine can move to a new state without consuming any input symbols. This is done through what is known as an ε-transition. An ε-transition allows the automaton to change states without any input, hence the name "Non-deterministic Finite Automaton with ε-transitions".

The automaton that allows transformation to a new state without consuming any input symbols is known as a Non-deterministic Finite Automaton with ε-transitions (NFA-ε). Here are the steps to understand this:

1. An automaton is a mathematical model of computation. It's a machine that takes a string of symbols as input and performs a sequence of state transitions based on the rules defined for the machine.

2. A Non-deterministic Finite Automaton (NFA) is a type of automaton where the machine can be in multiple states at once. It has the ability to make decisions on state transitions that are not uniquely determined by the input symbol.

3. An ε-transition is a special kind of state transition used in NFA where the automaton makes a transition to a new state without consuming an input symbol. The symbol ε represents an empty string.

4. Therefore, a Non-deterministic Finite Automaton with ε-transitions (NFA-ε) is an automaton that allows transformation to a new state without consuming any input symbols.